Automotive industry in the United Kingdom

The automotive industry in the United Kingdom is now best known for premium and sports car marques including: Aston Martin, McLaren, Bentley, Rolls-Royce, Jaguar, Land Rover, Mini and Lotus. Specialised sports car companies include: Ariel, BAC, Morgan, Caterham, AC Cars, Gordan Murray, TVR, Noble, Radical, Ginetta, Ultima Sports, Westfield, Lister, Arash and David Brown. Volume car manufacturers with a major presence in the UK include: Nissan, Toyota, Mini and Vauxhall. Commercial vehicle manufacturers active in the UK include Alexander Dennis, Dennis Eagle, IBC Vehicles, Leyland Trucks, TEVVA and the London Electric Vehicle Company.
In 2018 the UK automotive manufacturing sector had a turnover of £82 billion, generated £18.6 billion in value to the UK economy and produced around 1.5 million passenger vehicles and 85,000 commercial vehicles. In that year around 168,000 people were directly employed in automotive manufacturing in the UK, with a further 823,000 people employed in automotive supply, retail and servicing.
The UK is a major centre for engine manufacturing, and in 2018 around 2.71 million engines were produced in the country. The UK has a significant presence in auto racing and the UK motorsport industry currently employs around 38,500 people, comprises around 4,500 companies and has an annual turnover of around £6 billion.
The origins of the UK automotive industry date back to the final years of the 19th century. By the 1950s, the UK was the second-largest manufacturer of cars in the world (after the United States), and the largest exporter. However, in subsequent decades the industry experienced considerably lower growth than competitor nations such as France, Germany and Japan, and by 2008 the UK was the 12th-largest producer of cars measured by volume. Since the early 1990s, many British car marques have been invested in by international companies including BMW (Mini and Rolls-Royce), Tata (Jaguar and Land Rover) and Volkswagen Group (Bentley).
Famous and iconic British cars include the Aston Martin DB5, Aston Martin V8 Vantage, Bentley 4½ Litre, Jaguar E-Type, Land Rover Defender, Lotus Esprit, McLaren F1, MGB, original two-door Mini, Range Rover, Rolls-Royce Phantom III and Rover P5. Notable British car designers include David Bache, Dick Burzi, Laurence Pomeroy, John Polwhele Blatchley, Ian Callum, Colin Chapman, Alec Issigonis, Charles Spencer King and Gordon Murray.
History.
1880 to 1900.
The inception of the British motor industry can be traced back to the mid-1880s when there were several key developments. One development was when Frederick Simms, a London-based consulting engineer, became friends with Gottlieb Daimler, who had, in 1885, patented a successful design for a high-speed petrol engine. Simms acquired the British rights to Daimler's engine and associated patents and from 1891 successfully sold launches using these Cannstatt-made motors from Eel Pie Island in the Thames. In 1893 he formed "The Daimler Motor Syndicate Limited" for his various Daimler-related enterprises.
In June 1895, Simms and his friend Evelyn Ellis promoted motor cars in the United Kingdom by bringing a Daimler-engined "Panhard & Levassor" to England and in July it completed, without police intervention, the first British long-distance motorcar journey from Southampton to Malvern.
Simms' documented plans to manufacture Daimler motors and Daimler Motor Carriages (in Cheltenham) were taken over, together with his company and its Daimler licences, by London company-promoter H J Lawson. Lawson contracted to buy "The Daimler Motor Syndicate Limited" and all its rights and on 14 January 1896 formed and in February successfully floated in London "The Daimler Motor Company Limited". It then purchased from a friend of Lawson a disused cotton mill in Coventry for car engine and chassis manufacture where, it is claimed, the UK's first serial production car was made.
George Lanchester produced one of the first British cars between 1895 and 1896 having a single-cylinder 1306cc engine, he went on to sell the first car with disc brakes. In 1891 Richard Stephens, a mining engineer from South Wales, returned from a commission in Michigan to establish a bicycle works in Clevedon, Somerset. Whilst in the United States, he had seen the developments in motive power and by 1897 he had produced his first car. This was entirely of his own design and manufacture, including the two-cylinder engine, apart from the wheels which he bought from Starley in Coventry. This was probably the first all-British car and Stephens set up a production line, manufacturing in all, twelve vehicles, including four- and six-seater cars and hackneys, and nine-seater buses.
Early motor vehicle development in the UK had been effectively stopped by a series of Locomotive Acts introduced during the 19th century which severely restricted the use of mechanically propelled vehicles on the public highways. Following intense advocacy by motor vehicle enthusiasts, including Harry J. Lawson of Daimler, the worst restrictions of these acts, (the need for each vehicle to be accompanied by a crew of three, and a speed limit in towns), was lifted by the Locomotives on Highways Act 1896. Under this regulation, "light locomotives" (those vehicles under 3 tons unladen weight) were exempt from the previous restrictions, and a higher speed limit – was set for them. To celebrate the new freedoms Lawson organised the Emancipation Run held on 14 November 1896, the day the new Act came into force. This occasion has been commemorated since 1927 by the annual London to Brighton Veteran Car Run.
1900 to 1939.
The early British vehicles of the late-nineteenth century relied mainly upon developments from Germany and France. By 1900 however, the first all-British 4-wheel car had been designed and built by Herbert Austin as manager of The Wolseley Sheep Shearing Machine Company. In 1901, backed by (Vickers Limited) brothers 'Colonel Tom' and Albert Vickers [la], Austin started what became Wolseley Motors in Birmingham and was the UK's largest car manufacturer until Ford overtook them in 1913.
The great bulk of the pioneering car producers, many of them from the bicycle industry, got off to a shaky start. Of the 200 British makes of car that had been launched up until 1913, only about 100 of the firms were still in existence. In 1910, UK vehicle production was 14,000 units. By 1913, Henry Ford had built a new factory in Manchester and was the leading UK carmaker, building 7,310 cars that year, followed by Wolseley at 3,000, Humber (making cars since 1898 in Coventry) at 2,500, Rover (Coventry car maker since 1904) at 1,800 and Sunbeam (producing cars since 1901) at 1,700, with the plethora of smaller producers bringing the 1913 total up to about 16,000 vehicles. Car production virtually came to an end during the war years 1914–1918, although the requirements of war production led to the development of new mass-production techniques in the motor industry.
By 1922, there were 183 motor companies in the UK, and by 1929, following the slump years, there were 58 companies remaining. In 1929, production was dominated by Morris (founded by William Morris in 1910 in Oxford) and Austin (founded by Herbert Austin in Birmingham in 1905 after he left Wolseley) which between them produced around 60% of total UK output. Singer (Coventry motorcycle manufacturer started building cars in 1905) followed in third place that year with 15% of production.
In 1932, the UK overtook France to become Europe's largest car producer (a position which it retained until 1955). In 1937, the UK produced 379,310 passenger cars and 113,946 commercial vehicles. To celebrate the granting of his peerage, William Morris upon becoming Viscount Nuffield, reorganised his motor vehicle companies in 1938, which by then included not only Morris Motors and MG, but also Wolseley and Riley (bicycle company founded in Coventry in 1890 and making cars since 1906), into the Nuffield Organization. In 1939, the top producers were Morris: 27%, Austin: 24%, Ford: 15%, Standard (founded in Coventry in 1903): 13%, Rootes (which had acquired Humber and Sunbeam): 11%, Vauxhall (building cars since 1903, acquired by GM in 1925): 10%.
1939 to 1955.
During the Second World War, car production in the UK gave way to commercial and military vehicle production, and many motor vehicle plants were converted to aircraft and aero engine production. Following the war, the UK Government had nationalised the steel industry; where priority was given to supplying foreign-revenue-raising export businesses. In 1947, steel was available only to businesses which exported at least 75% of their production. This, coupled with the inevitably limited competition from continental Europe, and with demand for new vehicles in America and in Australia being greater than the American industry alone could supply, resulted in British vehicle exports reaching record levels and the UK became the world's largest motor vehicle exporter. In 1937, the UK provided 15% of world vehicle exports. By 1950, a year in which 75% of British car production and 60% of its commercial vehicle production was exported, the UK provided 52% of the world's exported vehicles.
This situation remained until the mid-1950s, by which time the American industry production had caught up with American demand, and European production was recovering. By 1952, the American-owned producers in the UK (Ford and GM's Vauxhall) had between them a 29% share of the British market, which exceeded the share of either of the UK's two top domestically owned manufacturers. It was in that context that Viscount Nuffield agreed to the merger of his company, the Nuffield Organization, with Austin, to form the British Motor Corporation (BMC). Thus BMC, comprising Austin, Morris, MG, Riley and Wolseley was formed in 1952 and commanded a 40% share of the British market. German production was increasing yearly, and by 1953 it had exceeded that of France, and by 1956 it had overtaken that of the UK.
1955 to 1968.
By 1955 five companies produced 90% of the UK's motor vehicle output: BMC, Ford, Rootes, Standard-Triumph and Vauxhall. Of the dozen or so smaller producers Rover and Jaguar were strong niche producers. By 1960 the UK had dropped from being the world's second largest motor vehicle producer into third place. Labour-intensive methods, and wide model ranges hindered opportunities to reduce manufacturing costs – the UK's unit costs were higher than those of their major Japanese, European and American competitors. Although rationalisation of motor vehicle companies had started, full integration did not occur. BMC continued to produce vehicles under the marque names of its incorporated companies, many of which competed with each other. Standard-Triumph's attempts to reduce costs by embracing a modern volume production strategy almost led to their bankruptcy in 1960, the result was that they were purchased by the commercial vehicle manufacturing company Leyland Motors. In 1966, BMC and Jaguar came together, to form British Motor Holdings (BMH). Leyland had achieved some sales success with Leyland-Triumph and in 1967 it acquired Rover. By 1966 the UK had slipped to become the world's fourth largest motor vehicle producer. Following a gradual process which had begun in 1964, Chrysler UK (CUK) had fully acquired Rootes by 1967.
In the context of BMC's wide, complex, and expensive-to-produce model range, Ford's conventionally designed Cortina challenging for the number one spot in the domestic market, and the heavy reliance of the British economy on motor vehicle production, in 1968 the Government brokered the merger of the successful Leyland-Triumph-Rover and the struggling BMH, to form Europe's fourth-largest car maker, the British Leyland Motor Corporation (BLMC). The new company announced its intention to invest in a new volume car range, and to equip its factories with the latest capital-intensive production methods.
BMC's Mini, designed by Alec Issigonis, had revolutionized the small car market in 1959, and the car remained among the UK's best selling cars for more than 20 years after its launch, the last version finally rolling off the production line on 4 October 2000 after a run of 41 years. The Rootes Group launched the similar-sized Hillman Imp four years later, but by the end of the 1960s Ford and Vauxhall had yet to launch a comparable product, and even with foreign imports slowly starting to gain ground on the British market, Italy's Fiat 500 was one of the few comparable alternatives to the virtual monopoly of the Mini and Hillman Imp in this sector of the market.
Also designed by Alec Issigonis was the Morris Minor, which was heavily updated in 1956 having originally gone into production in 1948. It earned a reputation for low running costs, good reliability and competitive pricing, and continued to sell well throughout the 1960s in spite of the popularity of BMC's 1100/1300 range which was launched in 1962, The Morris Minor was also the first British car to reach one million in production in 1961 with this record number reached a special model of the Morris Minor was created and sent to all of the main dealerships under the name "Morris Million".
Ford's competitor in this sector was the Anglia, which featured unconventional styling but was still one of the country's most successful cars from its launch in 1959 up to the end of production in 1967, after which it was replaced by the Escort. Other British competitors in this sector were the Vauxhall Viva and Hillman Minx.
Larger family cars enjoyed strong sales in the 1960s, namely the Ford Cortina (launched in 1962), Austin/Morris 1800 (1964) and Vauxhall Victor (1957). Later in the 1960s, the Rootes Group launched a new competitor in this growing sector of the market - the Hillman Hunter.
The Rover P6, launched in 1963 and the first winner of the European Car of the Year award, was arguably the most popular luxury model in the UK during the 1960s.
The iconic Jaguar E-Type sports car, designed by Malcolm Sayer, with a top speed of and the choice of a coupe or roadster bodystyle, was launched in 1961 and would remain in production until 1975. Cheaper sports cars also enjoyed strong sales during the 1960s, including the MG B and Triumph Spitfire which were launched in the early part of the decade, and the Ford Capri which was launched just before the decade's end.
The 1960s saw a slow but sure increase in the popularity of foreign cars on the British market. Volkswagen of West Germany had imported the iconic Beetle to Britain since 1953; this car was first launched in 1937 as a "people's car" for the German market under the Nazi regime. Its arrival on the UK market less than a decade after the end of World War II was met with hostility, with many examples being vandalised soon after being distributed, but it quickly became popular, with nearly 10,000 being sold in 1959. Volkswagen also began importing examples of its people carrier and van models, and by 1963 had sold 100,000 cars in Britain.Renault of France had actually built UK market versions of its cars at a site in Acton, West London, from 1902 until 1962, but its popularity actually increased after the end of UK production, helped by the arrival of the Renault 4 minicar in 1961 and the world's first production hatchback model, the Renault 16, in 1965. By the end of the decade, it had launched a smaller hatchback model, the Renault 6, and a mid-range saloon, the Renault 12, and was continuing to grow in popularity. Renault's French rival Peugeot also enjoyed success in the 1960s with its 404 saloon and even more so with its successor, the 504, which was launched in 1968. This set the scene for even more sales for foreign carmakers on the UK market during the next two decades, as their market share continued to grow.
Japanese cars also started to appear on the UK market during the 1960s, although they were a rare on British roads until exploding in popularity during the early 1970s. The Daihatsu Compagno was the first Japanese car to be sold in Britain when imports began during 1964. This car was not popular with British buyers and was withdrawn from sale within a few years, although Daihatsu would return to the UK market in the early 1980s. A year later, Toyota became the second Japanese carmaker to import cars to Britain. It was followed shortly afterwards by Nissan (which used the Datsun brand for the UK market) and Mazda. Honda was also enjoying great success on the motorcycle market by this stage, although it didn't start importing passenger cars to the UK until 1972.
1968 to 1987.
By 1968, UK motor vehicle production was dominated by four companies: BLMC, Chrysler (UK), Ford, and Vauxhall (GM). The Rootes Group had taken on the name Chrysler UK after its takeover by the American car giant Chrysler, which had also taken over French carmaker Simca.
The national champion, BLMC (British Leyland from 1968), was handicapped in its attempts to modernise by internal rivalries. Unattractive new products (particularly the Austin Allegro and Morris Marina) which were widely criticised by the motoring press, retention of legacy marques and models, labour disputes, quality issues, supplier problems and inefficient use of new equipment thwarted the dream of efficient high volume production. Increased overseas competition and high unit costs led to lowered profits, which in turn jeopardised investment plans. Although the cars continued to sell well in Britain, they were less popular on overseas markets. As well as that, the company often produced several cars to compete in the same market sector. For instance, it produced four competitors for the Ford Cortina at the same time - the Morris Marina, Austin Maxi, Triumph Dolomite and the Princess.
Japanese cars, particularly the Datsun badged cars built by Nissan enjoyed a strong surge in popularity during the first half of the 1970s, while French carmaker Renault and West German carmaker Volkswagen also enjoyed an upturn on the British market, helped by the arrival of well-received new cars, particularly the Renault 5 in 1972 and the Volkswagen Golf in 1974.
The fortunes of foreign carmakers on the British market were also assisted by the fact that most British manufacturers adopted the hatchback bodystyle, mostly featuring front-wheel drive, considerably later than their continental rivals. For instance, the arrival of the front-wheel drive Volkswagen Golf hatchback in 1974 came four years before any of the four British-based carmakers had launched an equivalent car. By the time the first small British-built hatchback, the Vauxhall Chevette, was launched in 1975, the French Renault 5 had already been in production for three years. However, British Leyland's larger Austin Maxi had been sold with a hatchback and front-wheel drive since its 1969 launch, although it sold similar-sized cars like the Morris Marina and Triumph Dolomite alongside it as a rear-wheel drive saloon alternative, with the Dolomite being sold further upmarket than the Marina. For buyers wanting six-cylinder and larger four-cylinder engines, the Princess was launched in 1975. Chrysler launched the Alpine for this market sector in 1975, featuring front wheel drive and a hatchback, but kept the Hunter in production alongside it until 1979 for buyers who still preferred rear-wheel drive and a saloon or estate bodystyle.
At the luxury end of the market, British Leyland was actually one of the first manufacturers in the world to put a hatchback on an upmarket car when it launched the Rover SD1 in 1976. This car signalled the beginning of rationalisation at British Leyland, with the SD1 replacing two model ranges - the Rover P6 and Triumph 2000/2500.
The popularity of Nissan's range of Datsun-badged cars in the 1970s was largely down to their low prices, cheap running costs, good equipment levels and a reputation for better reliability than most British cars, although these cars also went on to gain a reputation for being prone to rust.
BLMC's share of the UK market dropped from 40% to 32% between 1971 and 1973, with its new Morris Marina and Austin Allegro family cars selling well on the British market but not proving popular on many export markets, with the motoring media being critical of the styling of these new models as well as questions regarding the level of quality.
By 1974, the UK's position as a world motor vehicle manufacturer had dropped to sixth place. In 1974, both BLMC and Chrysler UK appealed to the UK Government for financial help. The Government rejected the idea of a merger between the two companies, and instead Chrysler UK received a loan and BLMC was subjected to a series of studies to determine its future. The Government's official BLMC enquiry, led by Lord Ryder, suggested that BLMC's strategy was sound, but required huge state investment to improve productivity by providing mechanisation and improving labour relations.
Despite the effective nationalisation of BLMC as British Leyland (BL) in 1975, the recovery never happened. Chrysler sold its European interests (including those in the UK) to Peugeot in 1978, to allow it to concentrate on its own difficulties in the United States. The UK interests were renamed Peugeot-Talbot, with production of the Chrysler-developed cars continuing, with the last Rootes-developed car, the Avenger, being discontinued in 1981. Peugeot also developed a saloon version of the Alpine called the Solara, and also launched the larger Tagora, which had been in development by Chrysler when it sold its European operations. It also replaced the entry-level Sunbeam with the Peugeot based Samba in 1981.
As in most other developed countries, the 1970s saw major changes to the cars produced in the UK. Front-wheel drive, which had been pioneered by BMC on several new models between 1959 and 1965, now became a common feature on family cars after decades of producing only rear-wheel drive models. The hatchback bodystyle, which had debuted in Europe on the French Renault 16 in 1965, became more popular, with many of Britain's best-selling cars being available with a hatchback by the early-1980s.
Many Ford and Vauxhall models were also being produced at their parent company's continental factories by 1980. Ford had switched Capri and Granada production to Germany by this stage, while production of its new Fiesta supermini was divided between Britain, West Germany and a new plant in Spain from its 1976 launch. General Motors had not only decided to make its Vauxhall and Opel badged cars mechanically identical during the 1970s, but it had also imported some of its Vauxhall-badged cars from Opel factories in West Germany and Belgium, and its Corsa supermini (Vauxhall Nova in the UK) was solely assembled at a factory in Zaragoza, Spain, which opened in 1982. British Leyland's overseas outposts in countries like Italy (where cars were produced under the Innocenti brand) were gradually closed down or sold to other carmakers, so by the 1980s; it was entirely a British-based operation.
By the end of the 1970s, Ford, Peugeot-Talbot and Vauxhall (GM) were well-integrated with their parent companies' other European operations. BL stood alone in the UK as an increasingly junior player. As part of the drive for increased productivity in the late-1970s, BL reduced its workforce and number of plants, and strived to centralise its management activities. The city of Coventry suffered particularly badly, with many thousands becoming unemployed after the closure of the Triumph car factory in the city in 1980.
In 1979, BL struck a collaboration deal with Honda to share the development and production of a new mid-sized car (Triumph Acclaim/Honda Ballade), which was launched in 1981. The new car combined Honda engine and transmission designs with a BL body, as did its successor model - the Rover 200 Series - in 1984. The next plan was to work on a new luxury car together, the end product being the Rover 800 Series, which arrived in 1986.
Although UK politics changed in 1979 with the election of the Conservative Party, the UK Government continued to support BL with funds for the development of a new mass-market model range (Mini Metro, Maestro, Montego and another Honda collaboration the Rover 800), which were all launched between 1980 and 1986. The Metro was the most successful of these cars.
Car assembly, with the exception of Jaguar, was concentrated into two central plants – Longbridge and Cowley. In July 1986, BL was renamed the Rover Group.
By the mid-1980s, front-wheel drive was now the standard on mass market cars, with most new models having a hatchback bodystyle as at least an option. Although Ford had adopted front-wheel drive for its new Spanish built Fiesta supermini in 1976 and the third generation Escort in 1980, it had curiously retained rear-wheel drive for its larger Sierra (the Cortina replacement) in 1982, although the Sierra did feature a hatchback bodystyle and was not available as a saloon until 1987. In 1983, it recognised the continuing demand for smaller and medium-sized family saloons by introducing the Orion, which was based on the Escort floorpan.
The supermini sector had expanded rapidly since the early-1970s. BMC's Mini had remained popular beyond its twentieth anniversary, but successor organisation British Leyland had started work on a more modern and practical alternative by the mid-1970s, the final result being the Austin Metro in 1980 - the new car featured more modern styling and a hatchback bodystyle. Chrysler Europe had axed the long-running Hillman Imp (launched by the Rootes Group in 1963) in 1976 and replaced it with the Chrysler Sunbeam hatchback a year later. General Motors had already adopted this bodystyle with the Vauxhall Chevette (which was also available as a saloon or estate) and Ford with the Fiesta. Comparable foreign products like the Fiat 127, Renault 5 and Volkswagen Polo were also proving popular in the UK.
Ford had now divided its European operations between its British factories and other European plants in Spain, Belgium and West Germany. General Motors had started importing some of its West German and Belgian built Opel products to the UK to be badged as Vauxhalls, and by 1983 its Nova supermini (badged as the Opel Corsa on the continent) was built solely in its Spanish factory. Peugeot was dividing production of most of the Talbot badged vehicles between the Ryton plant near Coventry (the Linwood plant in Scotland closed in 1981) and its French factories by the early-1980s, and started producing its own models at Coventry in 1985 after deciding to axe the Talbot marque due to falling sales.
Foreign carmakers continued to gain ground on the British market during the 1980s, with the likes of Renault, Peugeot, Citroen (France), Volvo (Sweden), Volkswagen (West Germany) and Fiat (Italy) proving particularly popular.
The Russian-built Lada, first sold in the UK in 1974, also sold well, despite its outdated Fiat-sourced design; with buyers mostly being attracted by its low price. By the late-1980s, with the four-wheel drive Niva and a front-wheel drive hatchback, the Samara, complementing the long-running Riva, Lada sales in Britain had amounted to more than 30,000 a year (some 1.5% of the new car market), but tailed off after 1990 as a result of growing competition and a lack of new model launches. Imports to Britain finally ceased in 1997 due to Lada's difficulties in meeting emissions requirements. Skoda also enjoyed similarly decent sales of its well-priced rear-engined saloon cars during the 1970s and 1980s, going from strength to strength in the 1990s following its takeover by Volkswagen and the launch of new model ranges with modern technology and styling. Zastava's Yugo-badged cars, based on Fiat designs from the 1970s, also sold reasonably well in Britain during the 1980s, but the carmaker was forced to halt imports in 1992 due to sanctions imposed on Yugoslavia as a result of the civil war there. Polish carmaker FSO imported its version of the Fiat 125 to Britain from 1975, later launching a hatchback model (the Polonez) alongside it. However, by 1998, Skoda was the only Eastern European carmaker still exporting cars to Britain, now competing with budget-priced Asian cars from the likes of Daewoo, Kia, Hyundai and Proton.
Nissan had axed the Datsun brand by 1984 and used its own name on all cars, and in 1986 opened a factory in Britain near Sunderland, which produced the mid-range Bluebird hatchbacks and saloons, although it was the Japanese-built Micra which was the company's best-selling car in Britain during the 1980s.
The decade also saw the arrival of purpose-built people carriers on the British market, starting with the Japanese Mitsubishi Space Wagon in 1984, and then the market-leading Renault Espace in 1985, but by the end of the decade this type of vehicle still had only a very small share of the British market and there were still no British-built people carriers available, although a few seven-seater estate models including Austin Rover's Montego were being produced.
The decade also saw a fall in demand for sports cars, perhaps due to the rising popularity of "hot hatchbacks" (high performance versions of hatchback cars), and so a number of manufacturers pulled out of the sports car market. British Leyland finished production of its MG and Triumph sports cars early in the decade, with no replacement. General Motors had launched coupe versions of its Cavalier mid-range model in the 1970s, but did not produce any equivalent models of the MK2 Cavalier which arrived in 1981. It did, however, continue to offer the German-built Opel Manta to British buyers until the end of production in 1988, replacing it with the Calibra (also built in Germany) a year later. Ford had enjoyed success in the 1970s with its Capri coupe, but this declined in popularity after 1980 and when production ended in 1986, there was no direct replacement.
As well as the rebranding of the former Rootes Group and its eventual integration into Peugeot, the 1980s also saw the disappearance of several long-established car brands. Production of MG sports cars finished when the Abingdon factory closed in 1980, although the brand was quickly revived on higher performance versions of the Metro, Maestro and Montego. 1980 also saw the closure of the Triumph factory at Canley, Coventry, although the marque survived until 1984 - the same year that the Morris marque was discontinued after more than seventy years. The Morris Ital's successor, the Montego, was sold under the Austin and MG brands, while the Triumph Acclaim's successor was sold as the Rover 200 Series. By 1988, however, the Austin marque had also been phased out, with the former Austin-badged products now being incorporated into the Rover brand.
General Motors enjoyed an upturn in Britain during the 1980s, as its Vauxhall-badged cars increased their market share and the company's image also improved. At the beginning of 1980, it replaced the Viva with a new front-wheel drive range of hatchback and estates - the Astra, which was built in Britain and also in Opel factories on the continent. The MK2 Cavalier was launched in 1981, and became the company's best selling car of the decade. Its replacement for the Chevette was the Nova, a rebadged version of the Spanish built Opel Corsa, which was launched in 1983. The MK2 Astra was voted European Car of the Year shortly after its launch in 1984, as was the flagship MK2 Carlton (Opel Omega on the continent) two years later.
1987 to 2001.
In July 1986, Nissan became the first Japanese carmaker to set up a production facility in Europe, when it opened a new plant in Sunderland. The plant initially produced the Bluebird and from 1990 its successor, the Primera, with the MK2 Micra joining it in 1992. Toyota opened a new plant in Burnaston near Derby at the beginning of 1992.
Peugeot started production of the Peugeot 309 hatchback at Ryton (originally a Rootes Group factory) in October 1985, followed by the Peugeot 405 two years later. During the 1990s, production of the 306 and 206 also began at Ryton.
Honda's venture with Austin Rover/Rover Group saw a number of different designs shared between the two marques. The venture came to an end in February 1994 when British Aerospace sold Rover Group to the German carmaker BMW for £800 million. The takeover meant that, for the first time in 112 years, the United Kingdom no longer had a British-owned volume car maker. BMW's ownership of the Rover Group saw the development of several newer, more upmarket models, giving the British brand an image to match that of its parent company. BMW also revived the MG marque in 1995 on a new affordable sports car, the MGF, as well as strengthening Land Rover's position in the off-roader market. In March 2000 BMW controversially announced the break-up of the Rover Group. It retained the rights to the Mini marque, while selling Land Rover to Ford. The MG and Rover marques were sold to the Phoenix Consortium, who branded the remains of the group as MG Rover and concentrated all production at the Longbridge plant. After the split from Rover, Honda continued making the Civic range in the UK at a new plant in Swindon.
Ford acquired Aston Martin for an undisclosed sum in September 1987 and Jaguar for US$2.38 billion in November 1989. Production of the new small Jaguar, the X type, started at Halewood in late 2000. By the end of the century, Ford had also acquired Land Rover.
In 1998 Vickers plc put Rolls-Royce Motors, including Bentley, up for auction. Volkswagen Group won the auction with a bid of US$780 million, but Rolls-Royce plc, which had the right to block a transfer of the Rolls-Royce name to non-British owners, agreed to sell the rights to BMW for US$65 million. It was subsequently agreed that control of the Rolls-Royce marque would pass from Volkswagen to BMW in 2003.
In 1995, Ford finally entered the decade-old people carrier market with its Galaxy, which was built in Portugal alongside the identical Volkswagen Sharan and Seat Alhambra as part of a venture between Ford and Volkswagen. Vauxhall entered this sector of the market a year later with the American-built Sintra, but this was not popular with British buyers and was discontinued after just three years when the smaller, German-built Zafira was launched, and proved far more popular than Vauxhall's original entry into the MPV market.
The affordable sports car market enjoyed a revival in the 1990s after going into virtual hibernation in the 1980s. Sparked by the popularity of the Japanese-built Mazda MX-5 after its launch in 1989, Rover began development on a new sports car in the early 1990s, finally launching the MG F two-seater roadster in 1995, 15 years after the demise of the last volume MG sports cars. The 1996 Lotus Elise also enjoyed relatively strong sales in this market sector, as did the Vauxhall VX220 (based on the Elise) which was launched in 2000. Ford, which had exited the sports car market by 1987 with the demise of the Capri to concentrate on faster versions of its best-selling hatchbacks and saloons, returned to this market sector in 1994 with the American-built Probe, and then enjoyed more success with its smaller Puma between 1997 and 2002.
2001 to 2011.
In May 2000 Ford announced that passenger car assembly as its Ford Dagenham plant would cease in 2002, ending 90 years of Ford passenger car assembly in the UK. At the same time Ford announced that it would invest US$500 million in the expansion of a diesel engine factory at the site, making Dagenham its largest diesel engine center worldwide and creating about 500 new jobs to offset the 1,900 lost in vehicle assembly for a total loss of 1,400. In December 2004 Ford announced a further investment of £169 million in the Dagenham plant, increasing annual output to one million diesel engines.
The closure of Vauxhall's Luton car assembly plant in March 2003 left Ellesmere Port as the sole Vauxhall assembly plant remaining in the UK. General Motors also retained the former Bedford works in Luton for producing vans such as the Vivaro and the Movano as well as Renault and Nissan badged variants. In April 2007, it was confirmed that the Ellesmere Port would produce the next generation Astra from 2010.
Losses at Jaguar led to closure of the company's Browns Lane plant in Coventry in 2004. Spare capacity at Halewood allowed Land Rover Freelander production to be transferred there in 2006.
MG Rover spent the early part of the 2000s investigating possible ventures with other carmakers in order to develop a new range of cars. Proposed links with foreign organisations including Malaysian carmaker Proton failed to materialise, and by late 2004 Chinese carmaker SAIC Motor had shown an interest in taking over the Longbridge-based firm – which was now hundreds of millions of pounds in debt. Talks broke down and the firm went into receivership in April 2005 with the loss of more than 6,000 jobs. Three months later, the firm's assets were purchased by another Chinese carmaker – Nanjing Automobile – and Longbridge partially re-opened over the summer of 2007 with an initial workforce of around 250 preparing to restart production of the MG TF which was relaunched in August 2008.
In April 2006 Peugeot closed its Ryton plant and moved 206 production to Slovakia. In 2007, Ford sold Aston Martin to a British-led Consortium backed by Middle East investors, retaining a small stake in the company and agreeing to continue the supply of components including engines. In 2008 Ford sold Jaguar Land Rover to Tata Motors of India for £1.15 billion. In November 2009, Dutch sportscar maker Spyker Cars announced that it would be moving production from Zeewolde to Whitley, Coventry, and UK production began in February 2010.
In March 2010 McLaren Automotive unveiled its MP4-12C model, alongside plans to produce around 4,000 cars per year at its Woking factory by the middle of the decade. At the Paris Motor Show in September 2010 Lotus Cars unveiled five new models due to go on sale by 2016, alongside plans for an investment of £770 million over 10 years, the complete redevelopment of its Hethel factory and an increase in production from under 3,000 cars per year to 6,000 to 7,000. In December 2010 it was announced that Renault had sold its remaining 25% shareholding in its eponymous Formula 1 team to Lotus Cars, and that the team would be renamed Lotus Renault in 2011.
2011 to 2019.
In January 2011 BMW announced that it would be extending the Mini range with the launch of two new two-door sports crossover vehicles based on the Mini Paceman concept car, with a coupe version to enter production in 2011 and a roadster in 2012. In March 2011 Jaguar Land Rover announced that it would be hiring an additional 1,500 staff at its Halewood plant, and signed over £2 billion of supply contracts with UK-based companies, to enable production of its new Range Rover Evoque model. In April 2011 the MG Motor subsidiary of SAIC Motor announced that mass production had resumed at the Longbridge plant, as the first MG 6 to be produced in the United Kingdom came off the production line. In May 2011 Jaguar unveiled plans to build the C-X75 petrol-electric hybrid supercar in the UK from 2013, with production to be in association with Williams Grand Prix Engineering; Jaguar announced the cancellation of the project in December 2012 due to the ongoing global economic crisis.
In May 2011, Aston Martin Lagonda confirmed that it was planning to revive the Lagonda marque, with the launch of two or three new models. In an interview with Reuters in the same month, Carl-Peter Forster, the Chief Executive of Tata Motors, revealed that Jaguar Land Rover would be investing over £5 billion in product development over the succeeding five years.
In June, Nissan announced that the replacement for its Qashqai model would be designed and built in the UK, in a total investment of £192 million safeguarding around 6,000 jobs. In June BMW announced an investment of £500 million in the UK over the subsequent three years as part of an expansion of the Mini range to seven models. In September 2011, Jaguar Land Rover confirmed that it would be investing £355 million in the construction of a new engine plant near Wolverhampton, to manufacture a new family of four-cylinder petrol and diesel engines. Later in the same month it was announced that the Jensen marque would be revived, with a new version of the Interceptor to be built by CPP Holdings at the former Jaguar factory Browns Lane in Coventry. In November, Toyota announced plans to make the UK its sole European manufacturing base for hatchback versions of its next C-segment family car, resulting in the investment of over £100 million in its Burnaston plant and the creation of around 1,500 new jobs.
In September 2013 it was announced that a new National Automotive Innovation Campus would be built at the University of Warwick's main campus at a cost of £100 million, with £45 million to be contributed by Jaguar Land Rover.
In the half-year from January to June 2014, the UK had its best year in new car sales in 9 years. 1.28 million new cars were sold during the period, a rise of 10% compared to the same period in 2013. In 2014, more than 1.5 million cars were produced, the highest since 2007.
The Society of Motor Manufacturers and Traders (SMMT) figures show a total of 2.31 million new cars were registered in 2019, down 2.4% from the year before. It was the third consecutive year of decline, and the SMMT expects that trend to continue in 2020.
In the year 2019, the best selling vehicle in the UK was Ford Fiesta, followed by Volkswagen Golf, Ford Transit, Ford Focus, and Vauxhall Corsa.
In 2019, Honda announced that its Swindon plant will close by 2021.
In June 2019, Ford announced that it would close its Ford Bridgend Engine Plant by September 2020 due to a lack of demand for the "Dragon" engine produced there. The plant was closed on 25 September 2020.
From 2020.
In March 2021, Aston Martin announced that their electric sports models would be manufactured at their car plant in Gaydon, Warwickshire.
Assembly plants.
There are numerous small companies manufacturing a small number of cars such as David Brown Automotive, Lister Cars, Lightning Car Company and Atalanta Motors.
Car design.
The UK has a strong design and technical base, with several foreign companies basing some of their research and development resource in the UK, including:
Independent designers and design companies include:
Motorsport.
It has been estimated that there are about 4,000 companies in the UK involved in the manufacturing industry related to motorsport.
Formula One motor racing has made its home in the UK, with seven of the ten teams competing in the 2024 season based in or having their European headquarters in England:
Formula One engine suppliers:
Other major motorsports teams and organisations:
Inactive marques.
Currently inactive British automotive marques include:
Allard,
Alvis,
Armstrong Siddeley,
Austin,
Autovia,
Daimler,
DeLorean,
Gilbern,
Gordon-Keeble,
Healey,
Hillman,
Humber,
Jensen,
Jowett,
Lanchester,
Lea-Francis,
Morris,
Napier,
Reliant,
Riley,
Rover,
Singer,
Standard,
Sterling,
Sunbeam,
Sunbeam-Talbot,
Talbot,
Triumph,
TVR,
Vanden Plas,
Wolseley Motors.
Dealership groups.
There has been significant consolidation of car dealerships in the UK, leading to several large and notable dealership groups. As of June 2021, Sytner Group is the largest with a turnover of £4.92 billion.
Car market.
Despite the loss of mass-market British marques, car models that are built in the UK are generally popular in the UK sales charts, examples being the Nissan Qashqai.
As of 2014[ [update]] 2.45 million cars were sold in the UK, with the Volkswagen Group having a 20.8% share, Ford Motor Company having 13.2% and General Motors having 11.3%. Subcompact and compact cars were the most popular sizes although SUVs were gaining a significant foothold. The Fiat 500 was the best selling A-segment product, Ford Fiesta the best selling in the B-segment, Ford Focus best selling in the C-segment and BMW 3 Series best selling in the D-segment.
In 2019, the best selling car model in the UK was Ford Fiesta followed by Volkswagen Golf and Ford Focus.
References.
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External links.
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Probability
Branch of mathematics concerning chance and uncertainty
Probability is a branch of mathematics and statistics concerning events and numerical descriptions of how likely they are to occur. The probability of an event is a number between 0 and 1; the larger the probability, the more likely an event is to occur. This number is often expressed as a percentage (%), ranging from 0% to 100%. A simple example is the tossing of a fair (unbiased) coin. Since the coin is fair, the two outcomes ("heads" and "tails") are both equally probable; the probability of "heads" equals the probability of "tails"; and since no other outcomes are possible, the probability of either "heads" or "tails" is 1/2 (which could also be written as 0.5 or 50%).
These concepts have been given an axiomatic mathematical formalization in "probability theory", which is used widely in areas of study such as statistics, mathematics, science, finance, gambling, artificial intelligence, machine learning, computer science, game theory, and philosophy to, for example, draw inferences about the expected frequency of events. Probability theory is also used to describe the underlying mechanics and regularities of complex systems.
Etymology.
The word "probability" derives from the Latin , which can also mean "probity", a measure of the authority of a witness in a legal case in Europe, and often correlated with the witness's nobility. In a sense, this differs much from the modern meaning of "probability", which in contrast is a measure of the weight of empirical evidence, and is arrived at from inductive reasoning and statistical inference.
Interpretations.
When dealing with random experiments – i.e., experiments that are random and well-defined – in a purely theoretical setting (like tossing a coin), probabilities can be numerically described by the number of desired outcomes, divided by the total number of all outcomes. This is referred to as theoretical probability (in contrast to empirical probability, dealing with probabilities in the context of real experiments). For example, tossing a coin twice will yield "head-head", "head-tail", "tail-head", and "tail-tail" outcomes. The probability of getting an outcome of "head-head" is 1 out of 4 outcomes, or, in numerical terms, 1/4, 0.25 or 25%. However, when it comes to practical application, there are two major competing categories of probability interpretations, whose adherents hold different views about the fundamental nature of probability:
History.
The scientific study of probability is a modern development of mathematics. Gambling shows that there has been an interest in quantifying the ideas of probability throughout history, but exact mathematical descriptions arose much later. There are reasons for the slow development of the mathematics of probability. Whereas games of chance provided the impetus for the mathematical study of probability, fundamental issues are still obscured by superstitions.
According to Richard Jeffrey, "Before the middle of the seventeenth century, the term 'probable' (Latin "probabilis") meant "approvable", and was applied in that sense, univocally, to opinion and to action. A probable action or opinion was one such as sensible people would undertake or hold, in the circumstances." However, in legal contexts especially, 'probable' could also apply to propositions for which there was good evidence.
The sixteenth-century Italian polymath Gerolamo Cardano demonstrated the efficacy of defining odds as the ratio of favourable to unfavourable outcomes (which implies that the probability of an event is given by the ratio of favourable outcomes to the total number of possible outcomes).
Aside from the elementary work by Cardano, the doctrine of probabilities dates to the correspondence of Pierre de Fermat and Blaise Pascal (1654). Christiaan Huygens (1657) gave the earliest known scientific treatment of the subject. Jakob Bernoulli's "Ars Conjectandi" (posthumous, 1713) and Abraham de Moivre's "Doctrine of Chances" (1718) treated the subject as a branch of mathematics. See Ian Hacking's "The Emergence of Probability" and James Franklin's "The Science of Conjecture" for histories of the early development of the very concept of mathematical probability.
The theory of errors may be traced back to Roger Cotes's "Opera Miscellanea" (posthumous, 1722), but a memoir prepared by Thomas Simpson in 1755 (printed 1756) first applied the theory to the discussion of errors of observation. The reprint (1757) of this memoir lays down the axioms that positive and negative errors are equally probable, and that certain assignable limits define the range of all errors. Simpson also discusses continuous errors and describes a probability curve.
The first two laws of error that were proposed both originated with Pierre-Simon Laplace. The first law was published in 1774, and stated that the frequency of an error could be expressed as an exponential function of the numerical magnitude of the error – disregarding sign. The second law of error was proposed in 1778 by Laplace, and stated that the frequency of the error is an exponential function of the square of the error. The second law of error is called the normal distribution or the Gauss law. "It is difficult historically to attribute that law to Gauss, who in spite of his well-known precocity had probably not made this discovery before he was two years old."
Daniel Bernoulli (1778) introduced the principle of the maximum product of the probabilities of a system of concurrent errors.
Adrien-Marie Legendre (1805) developed the method of least squares, and introduced it in his "Nouvelles méthodes pour la détermination des orbites des comètes" ("New Methods for Determining the Orbits of Comets"). In ignorance of Legendre's contribution, an Irish-American writer, Robert Adrain, editor of "The Analyst" (1808), first deduced the law of facility of error,
formula_1
where formula_2 is a constant depending on precision of observation, and formula_3 is a scale factor ensuring that the area under the curve equals 1. He gave two proofs, the second being essentially the same as John Herschel's (1850). Gauss gave the first proof that seems to have been known in Europe (the third after Adrain's) in 1809. Further proofs were given by Laplace (1810, 1812), Gauss (1823), James Ivory (1825, 1826), Hagen (1837), Friedrich Bessel (1838), W.F. Donkin (1844, 1856), and Morgan Crofton (1870). Other contributors were Ellis (1844), De Morgan (1864), Glaisher (1872), and Giovanni Schiaparelli (1875). Peters's (1856) formula for "r", the probable error of a single observation, is well known.
In the nineteenth century, authors on the general theory included Laplace, Sylvestre Lacroix (1816), Littrow (1833), Adolphe Quetelet (1853), Richard Dedekind (1860), Helmert (1872), Hermann Laurent (1873), Liagre, Didion and Karl Pearson. Augustus De Morgan and George Boole improved the exposition of the theory.
In 1906, Andrey Markov introduced the notion of Markov chains, which played an important role in stochastic processes theory and its applications. The modern theory of probability based on measure theory was developed by Andrey Kolmogorov in 1931.
On the geometric side, contributors to "The Educational Times" included Miller, Crofton, McColl, Wolstenholme, Watson, and Artemas Martin. See integral geometry for more information.
Theory.
Like other theories, the theory of probability is a representation of its concepts in formal terms – that is, in terms that can be considered separately from their meaning. These formal terms are manipulated by the rules of mathematics and logic, and any results are interpreted or translated back into the problem domain.
There have been at least two successful attempts to formalize probability, namely the Kolmogorov formulation and the Cox formulation. In Kolmogorov's formulation (see also probability space), sets are interpreted as events and probability as a measure on a class of sets. In Cox's theorem, probability is taken as a primitive (i.e., not further analyzed), and the emphasis is on constructing a consistent assignment of probability values to propositions. In both cases, the laws of probability are the same, except for technical details.
There are other methods for quantifying uncertainty, such as the Dempster–Shafer theory or possibility theory, but those are essentially different and not compatible with the usually-understood laws of probability.
Applications.
Probability theory is applied in everyday life in risk assessment and modeling. The insurance industry and markets use actuarial science to determine pricing and make trading decisions. Governments apply probabilistic methods in environmental regulation, entitlement analysis, and financial regulation.
An example of the use of probability theory in equity trading is the effect of the perceived probability of any widespread Middle East conflict on oil prices, which have ripple effects in the economy as a whole. An assessment by a commodity trader that a war is more likely can send that commodity's prices up or down, and signals other traders of that opinion. Accordingly, the probabilities are neither assessed independently nor necessarily rationally. The theory of behavioral finance emerged to describe the effect of such groupthink on pricing, on policy, and on peace and conflict.
In addition to financial assessment, probability can be used to analyze trends in biology (e.g., disease spread) as well as ecology (e.g., biological Punnett squares). As with finance, risk assessment can be used as a statistical tool to calculate the likelihood of undesirable events occurring, and can assist with implementing protocols to avoid encountering such circumstances. Probability is used to design games of chance so that casinos can make a guaranteed profit, yet provide payouts to players that are frequent enough to encourage continued play.
Another significant application of probability theory in everyday life is reliability. Many consumer products, such as automobiles and consumer electronics, use reliability theory in product design to reduce the probability of failure. Failure probability may influence a manufacturer's decisions on a product's warranty.
The cache language model and other statistical language models that are used in natural language processing are also examples of applications of probability theory.
Mathematical treatment.
Consider an experiment that can produce a number of results. The collection of all possible results is called the sample space of the experiment, sometimes denoted as formula_4. The power set of the sample space is formed by considering all different collections of possible results. For example, rolling a die can produce six possible results. One collection of possible results gives an odd number on the die. Thus, the subset {1,3,5} is an element of the power set of the sample space of dice rolls. These collections are called "events". In this case, {1,3,5} is the event that the die falls on some odd number. If the results that actually occur fall in a given event, the event is said to have occurred.
A probability is a way of assigning every event a value between zero and one, with the requirement that the event made up of all possible results (in our example, the event {1,2,3,4,5,6}) is assigned a value of one. To qualify as a probability, the assignment of values must satisfy the requirement that for any collection of mutually exclusive events (events with no common results, such as the events {1,6}, {3}, and {2,4}), the probability that at least one of the events will occur is given by the sum of the probabilities of all the individual events.
The probability of an event "A" is written as formula_5, formula_6, or formula_7. This mathematical definition of probability can extend to infinite sample spaces, and even uncountable sample spaces, using the concept of a measure.
The "opposite" or "complement" of an event "A" is the event [not "A"] (that is, the event of "A" not occurring), often denoted as formula_8, formula_9, or formula_10; its probability is given by "P"(not "A") = 1 − "P"("A"). As an example, the chance of not rolling a six on a six-sided die is 1 – (chance of rolling a six) = 1 − = . For a more comprehensive treatment, see Complementary event.
If two events "A" and "B" occur on a single performance of an experiment, this is called the intersection or joint probability of "A" and "B", denoted as formula_11
Independent events.
If two events, "A" and "B" are independent then the joint probability is
formula_12
For example, if two coins are flipped, then the chance of both being heads is formula_13
Mutually exclusive events.
If either event "A" or event "B" can occur but never both simultaneously, then they are called mutually exclusive events.
If two events are mutually exclusive, then the probability of "both" occurring is denoted as formula_14 andformula_15If two events are mutually exclusive, then the probability of "either" occurring is denoted as formula_16 andformula_17
For example, the chance of rolling a 1 or 2 on a six-sided die is formula_18
Not (necessarily) mutually exclusive events.
If the events are not (necessarily) mutually exclusive thenformula_19Rewritten,formula_20
For example, when drawing a card from a deck of cards, the chance of getting a heart or a face card (J, Q, K) (or both) is formula_21 since among the 52 cards of a deck, 13 are hearts, 12 are face cards, and 3 are both: here the possibilities included in the "3 that are both" are included in each of the "13 hearts" and the "12 face cards", but should only be counted once.
This can be expanded further for multiple not (necessarily) mutually exclusive events. For three events, this proceeds as follows:formula_22It can be seen, then, that this pattern can be repeated for any number of events.
Conditional probability.
"Conditional probability" is the probability of some event "A", given the occurrence of some other event "B". Conditional probability is written formula_23, and is read "the probability of "A", given "B"". It is defined by
formula_24
If formula_25 then formula_23 is formally undefined by this expression. In this case formula_27 and formula_28 are independent, since formula_29 However, it is possible to define a conditional probability for some zero-probability events, for example by using a σ-algebra of such events (such as those arising from a continuous random variable).
For example, in a bag of 2 red balls and 2 blue balls (4 balls in total), the probability of taking a red ball is formula_30 however, when taking a second ball, the probability of it being either a red ball or a blue ball depends on the ball previously taken. For example, if a red ball was taken, then the probability of picking a red ball again would be formula_31 since only 1 red and 2 blue balls would have been remaining. And if a blue ball was taken previously, the probability of taking a red ball will be formula_32
Inverse probability.
In probability theory and applications, "Bayes' rule" relates the odds of event formula_33 to event formula_34 before (prior to) and after (posterior to) conditioning on another event formula_35 The odds on formula_33 to event formula_37 is simply the ratio of the probabilities of the two events. When arbitrarily many events formula_27 are of interest, not just two, the rule can be rephrased as "posterior is proportional to prior times likelihood", formula_39 where the proportionality symbol means that the left hand side is proportional to (i.e., equals a constant times) the right hand side as formula_27 varies, for fixed or given formula_28 (Lee, 2012; Bertsch McGrayne, 2012). In this form it goes back to Laplace (1774) and to Cournot (1843); see Fienberg (2005).
Relation to randomness and probability in quantum mechanics.
In a deterministic universe, based on Newtonian concepts, there would be no probability if all conditions were known (Laplace's demon) (but there are situations in which sensitivity to initial conditions exceeds our ability to measure them, i.e. know them). In the case of a roulette wheel, if the force of the hand and the period of that force are known, the number on which the ball will stop would be a certainty (though as a practical matter, this would likely be true only of a roulette wheel that had not been exactly levelled – as Thomas A. Bass' Newtonian Casino revealed). This also assumes knowledge of inertia and friction of the wheel, weight, smoothness, and roundness of the ball, variations in hand speed during the turning, and so forth. A probabilistic description can thus be more useful than Newtonian mechanics for analyzing the pattern of outcomes of repeated rolls of a roulette wheel. Physicists face the same situation in the kinetic theory of gases, where the system, while deterministic "in principle", is so complex (with the number of molecules typically the order of magnitude of the Avogadro constant ) that only a statistical description of its properties is feasible.
Probability theory is required to describe quantum phenomena. A revolutionary discovery of early 20th century physics was the random character of all physical processes that occur at sub-atomic scales and are governed by the laws of quantum mechanics. The objective wave function evolves deterministically but, according to the Copenhagen interpretation, it deals with probabilities of observing, the outcome being explained by a wave function collapse when an observation is made. However, the loss of determinism for the sake of instrumentalism did not meet with universal approval. Albert Einstein famously in a letter to Max Born: "I am convinced that God does not play dice". Like Einstein, Erwin Schrödinger, who discovered the wave function, believed quantum mechanics is a statistical approximation of an underlying deterministic reality. In some modern interpretations of the statistical mechanics of measurement, quantum decoherence is invoked to account for the appearance of subjectively probabilistic experimental outcomes.
Notes.
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References.
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Conditional probability
Probability of an event occurring, given that another event has already occurred
In probability theory, conditional probability is a measure of the probability of an event occurring, given that another event (by assumption, presumption, assertion or evidence) is already known to have occurred. This particular method relies on event A occurring with some sort of relationship with another event B. In this situation, the event A can be analyzed by a conditional probability with respect to B. If the event of interest is A and the event B is known or assumed to have occurred, "the conditional probability of A given B", or "the probability of A under the condition B", is usually written as P("A"|"B") or occasionally P"B"("A"). This can also be understood as the fraction of probability B that intersects with A, or the ratio of the probabilities of both events happening to the "given" one happening (how many times A occurs rather than not assuming B has occurred): formula_1.
For example, the probability that any given person has a cough on any given day may be only 5%. But if we know or assume that the person is sick, then they are much more likely to be coughing. For example, the conditional probability that someone sick is coughing might be 75%, in which case we would have that P(Cough) = 5% and P(Cough|Sick) = 75 %. Although there is a relationship between A and B in this example, such a relationship or dependence between A and B is not necessary, nor do they have to occur simultaneously.
P("A"|"B") may or may not be equal to P("A"), i.e., the unconditional probability or absolute probability of A. If P("A"|"B") = P("A"), then events A and B are said to be "independent": in such a case, knowledge about either event does not alter the likelihood of each other. P("A"|"B") (the conditional probability of A given B) typically differs from P("B"|"A"). For example, if a person has dengue fever, the person might have a 90% chance of being tested as positive for the disease. In this case, what is being measured is that if event B ("having dengue") has occurred, the probability of A ("tested as positive") given that B occurred is 90%, simply writing P("A"|"B") = 90%. Alternatively, if a person is tested as positive for dengue fever, they may have only a 15% chance of actually having this rare disease due to high false positive rates. In this case, the probability of the event B ("having dengue") given that the event A ("testing positive") has occurred is 15% or P("B"|"A") = 15%. It should be apparent now that falsely equating the two probabilities can lead to various errors of reasoning, which is commonly seen through base rate fallacies.
While conditional probabilities can provide extremely useful information, limited information is often supplied or at hand. Therefore, it can be useful to reverse or convert a conditional probability using Bayes' theorem: formula_2. Another option is to display conditional probabilities in a conditional probability table to illuminate the relationship between events.
Definition.
Conditioning on an event.
Kolmogorov definition.
Given two events A and B from the sigma-field of a probability space, with the unconditional probability of B being greater than zero (i.e., P("B") > 0), the conditional probability of A given B (formula_3) is the probability of "A" occurring if "B" has or is assumed to have happened. "A" is assumed to be the set of all possible outcomes of an experiment or random trial that has a restricted or reduced sample space. The conditional probability can be found by the quotient of the probability of the joint intersection of events A and B, that is, formula_4, the probability at which "A" and "B" occur together, and the probability of B:
formula_1.
For a sample space consisting of equal likelihood outcomes, the probability of the event "A" is understood as the fraction of the number of outcomes in "A" to the number of all outcomes in the sample space. Then, this equation is understood as the fraction of the set formula_6 to the set "B". Note that the above equation is a definition, not just a theoretical result. We denote the quantity formula_7 as formula_8 and call it the "conditional probability of A given B."
As an axiom of probability.
Some authors, such as de Finetti, prefer to introduce conditional probability as an axiom of probability:
formula_9.
This equation for a conditional probability, although mathematically equivalent, may be intuitively easier to understand. It can be interpreted as "the probability of "B" occurring multiplied by the probability of "A" occurring, provided that "B" has occurred, is equal to the probability of the "A" and "B" occurrences together, although not necessarily occurring at the same time". Additionally, this may be preferred philosophically; under major probability interpretations, such as the subjective theory, conditional probability is considered a primitive entity. Moreover, this "multiplication rule" can be practically useful in computing the probability of formula_6 and introduces a symmetry with the summation axiom for Poincaré Formula:
formula_11
Thus the equations can be combined to find a new representation of the :
formula_12
formula_13
As the probability of a conditional event.
Conditional probability can be defined as the probability of a conditional event formula_14. The Goodman–Nguyen–Van Fraassen conditional event can be defined as:
formula_15 and formula_16 represent states or elements of "A" or "B."
It can be shown that
formula_17
which meets the Kolmogorov definition of conditional probability.
Conditioning on an event of probability zero.
If formula_18, then according to the definition, formula_19 is undefined.
The case of greatest interest is that of a random variable Y, conditioned on a continuous random variable X resulting in a particular outcome x. The event formula_20 has probability zero and, as such, cannot be conditioned on.
Instead of conditioning on X being "exactly" x, we could condition on it being closer than distance formula_21 away from x. The event formula_22 will generally have nonzero probability and hence, can be conditioned on.
We can then take the limit
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For example, if two continuous random variables X and Y have a joint density formula_23, then by L'Hôpital's rule and Leibniz integral rule, upon differentiation with respect to formula_21:
formula_25
The resulting limit is the conditional probability distribution of Y given X and exists when the denominator, the probability density formula_26, is strictly positive.
It is tempting to "define" the undefined probability formula_27 using limit (1), but this cannot be done in a consistent manner. In particular, it is possible to find random variables X and W and values x, w such that the events formula_28 and formula_29 are identical but the resulting limits are not:
formula_30
The Borel–Kolmogorov paradox demonstrates this with a geometrical argument.
Conditioning on a discrete random variable.
Let X be a discrete random variable and its possible outcomes denoted V. For example, if X represents the value of a rolled dice then V is the set formula_31. Let us assume for the sake of presentation that X is a discrete random variable, so that each value in V has a nonzero probability.
For a value x in V and an event A, the conditional probability
is given by formula_32.
Writing
formula_33
for short, we see that it is a function of two variables, x and A.
For a fixed A, we can form the random variable formula_34. It represents an outcome of formula_32 whenever a value x of X is observed.
The conditional probability of A given X can thus be treated as a random variable Y with outcomes in the interval formula_36. From the law of total probability, its expected value is equal to the unconditional probability of A.
Partial conditional probability.
The partial conditional probability
formula_37
is about the probability of event
formula_38 given that each of the condition events
formula_39 has occurred to a degree
formula_40 (degree of belief, degree of experience) that might be different from 100%. Frequentistically, partial conditional probability makes sense, if the conditions are tested in experiment repetitions of appropriate length
formula_41. Such
formula_41-bounded partial conditional probability can be defined as the conditionally expected average occurrence of event
formula_38 in testbeds of length
formula_41 that adhere to all of the probability specifications
formula_45, i.e.:
formula_46
Based on that, partial conditional probability can be defined as
formula_47
where formula_48
Jeffrey conditionalization
is a special case of partial conditional probability, in which the condition events must form a partition:
formula_49
Example.
Suppose that somebody secretly rolls two fair six-sided dice, and we wish to compute the probability that the face-up value of the first one is 2, given the information that their sum is no greater than 5.
"Probability that" "D"1 = 2
Table 1 shows the sample space of 36 combinations of rolled values of the two dice, each of which occurs with probability 1/36, with the numbers displayed in the red and dark gray cells being "D"1 + "D"2.
"D"1 = 2 in exactly 6 of the 36 outcomes; thus "P"("D"1 = 2) = <templatestyles src="Fraction/styles.css" />6⁄36 = <templatestyles src="Fraction/styles.css" />1⁄6:
"Probability that" "D"1 + "D"2 ≤ 5
Table 2 shows that "D"1 + "D"2 ≤ 5 for exactly 10 of the 36 outcomes, thus "P"("D"1 + "D"2 ≤ 5) = <templatestyles src="Fraction/styles.css" />10⁄36:
"Probability that" "D"1 = 2 "given that" "D"1 + "D"2 ≤ 5
Table 3 shows that for 3 of these 10 outcomes, "D"1 = 2.
Thus, the conditional probability P("D"1 = 2 | "D"1+"D"2 ≤ 5) = <templatestyles src="Fraction/styles.css" />3⁄10 = 0.3:
Here, in the earlier notation for the definition of conditional probability, the conditioning event "B" is that "D"1 + "D"2 ≤ 5, and the event "A" is "D"1 = 2. We have formula_50 as seen in the table.
Use in inference.
In statistical inference, the conditional probability is an update of the probability of an event based on new information. The new information can be incorporated as follows:
This approach results in a probability measure that is consistent with the original probability measure and satisfies all the Kolmogorov axioms. This conditional probability measure also could have resulted by assuming that the relative magnitude of the probability of "A" with respect to "X" will be preserved with respect to "B" (cf. a Formal Derivation below).
The wording "evidence" or "information" is generally used in the Bayesian interpretation of probability. The conditioning event is interpreted as evidence for the conditioned event. That is, "P"("A") is the probability of "A" before accounting for evidence "E", and "P"("A"|"E") is the probability of "A" after having accounted for evidence "E" or after having updated "P"("A"). This is consistent with the frequentist interpretation, which is the first definition given above.
Example.
When Morse code is transmitted, there is a certain probability that the "dot" or "dash" that was received is erroneous. This is often taken as interference in the transmission of a message. Therefore, it is important to consider when sending a "dot", for example, the probability that a "dot" was received. This is represented by: formula_54 In Morse code, the ratio of dots to dashes is 3:4 at the point of sending, so the probability of a "dot" and "dash" are formula_55. If it is assumed that the probability that a dot is transmitted as a dash is 1/10, and that the probability that a dash is transmitted as a dot is likewise 1/10, then Bayes's rule can be used to calculate formula_56.
formula_57
formula_58
formula_59
Now, formula_60 can be calculated:
formula_61
Statistical independence.
Events "A" and "B" are defined to be statistically independent if the probability of the intersection of A and B is equal to the product of the probabilities of A and B:
formula_62
If "P"("B") is not zero, then this is equivalent to the statement that
formula_63
Similarly, if "P"("A") is not zero, then
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is also equivalent. Although the derived forms may seem more intuitive, they are not the preferred definition as the conditional probabilities may be undefined, and the preferred definition is symmetrical in "A" and "B". Independence does not refer to a disjoint event.
It should also be noted that given the independent event pair [A B] and an event C, the pair is defined to be conditionally independent if the product holds true:
formula_65
This theorem could be useful in applications where multiple independent events are being observed.
Independent events vs. mutually exclusive events
The concepts of mutually independent events and mutually exclusive events are separate and distinct. The following table contrasts results for the two cases (provided that the probability of the conditioning event is not zero).
In fact, mutually exclusive events cannot be statistically independent (unless both of them are impossible), since knowing that one occurs gives information about the other (in particular, that the latter will certainly not occur).
"These fallacies should not be confused with Robert K. Shope's 1978 "conditional fallacy", which deals with counterfactual examples that beg the question."
Common fallacies.
Assuming conditional probability is of similar size to its inverse.
In general, it cannot be assumed that "P"("A"|"B") ≈ "P"("B"|"A"). This can be an insidious error, even for those who are highly conversant with statistics. The relationship between "P"("A"|"B") and "P"("B"|"A") is given by Bayes' theorem:
formula_66
That is, "P"("A"|"B") ≈ "P"("B"|"A") only if "P"("B")/"P"("A") ≈ 1, or equivalently, "P"("A") ≈ "P"("B").
Assuming marginal and conditional probabilities are of similar size.
In general, it cannot be assumed that "P"("A") ≈ "P"("A"|"B"). These probabilities are linked through the law of total probability:
formula_67
where the events formula_68 form a countable partition of formula_69.
This fallacy may arise through selection bias. For example, in the context of a medical claim, let "S""C" be the event that a sequela (chronic disease) "S" occurs as a consequence of circumstance (acute condition) "C". Let "H" be the event that an individual seeks medical help. Suppose that in most cases, "C" does not cause "S" (so that "P"("S""C") is low). Suppose also that medical attention is only sought if "S" has occurred due to "C". From experience of patients, a doctor may therefore erroneously conclude that "P"("S""C") is high. The actual probability observed by the doctor is "P"("S""C"|"H").
Over- or under-weighting priors.
Not taking prior probability into account partially or completely is called "base rate neglect". The reverse, insufficient adjustment from the prior probability is "conservatism".
Formal derivation.
Formally, "P"("A" | "B") is defined as the probability of "A" according to a new probability function on the sample space, such that outcomes not in "B" have probability 0 and that it is consistent with all original probability measures.
Let Ω be a discrete sample space with elementary events {"ω"}, and let "P" be the probability measure with respect to the σ-algebra of Ω. Suppose we are told that the event "B" ⊆ Ω has occurred. A new probability distribution (denoted by the conditional notation) is to be assigned on {"ω"} to reflect this. All events that are not in "B" will have null probability in the new distribution. For events in "B", two conditions must be met: the probability of "B" is one and the relative magnitudes of the probabilities must be preserved. The former is required by the axioms of probability, and the latter stems from the fact that the new probability measure has to be the analog of "P" in which the probability of "B" is one - and every event that is not in "B", therefore, has a null probability. Hence, for some scale factor "α", the new distribution must satisfy:
Substituting 1 and 2 into 3 to select "α":
formula_73
So the new probability distribution is
Now for a general event "A",
formula_76
See also.
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References.
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Odds
Ratio of the probability of an event happening versus not happening
In probability theory, odds provide a measure of the probability of a particular outcome. Odds are commonly used in gambling and statistics. For example for an event that is 40% probable, one could say that the odds are