TITLE: Why is not the answer to all probability questions 1/2.
QUESTION [16 upvotes]: Ok, I know this is wrong, but I want someone to tell me why. 
Let's take a normal heads tails example of a fair coin. The probability of getting head = 1/2. And I write this is because, either it will be heads, or not. Hence two cases that makes it 1/2.
Now, I know I can't do this to all the cases. For example, the probability of getting a 2 when I roll a dice. I know the answer is 1/6 but why can't I do, either the outcome will be 2 or not. And in that case, my probability is 1/2.

REPLY [3 votes]: It's important to note that sometimes the wrong steps will give the right answer, by chance. 
Your statement of "The probability of getting heads = 1/2. And I write this is because, either it will be heads, or not." is faulty, even though it produces the correct answer. A more correct statement would be "either it will be heads, or it will be tails, with an equal chance for each. Therefore, 1/2." 
Compare to a die with 'heads' written on one face, and 'tails' written on the other five. In this case, still, either it will be heads or it will not -- and either it will be tails or it will not -- but because they are not equal probabilities, you have a 1/6 chance of heads and 5/6 chance of tails. It should be obvious that if five times as many sides say 'tails' then you have a five-times greater chance of getting tails. 
Which is a lengthy way of saying that "Either it's A or it's not A" doesn't properly weigh the two possibilities. Just because there are two possibilities doesn't mean each has an equal chance of being chosen. 
Otherwise, every day I'd have a 50% chance of becoming the supreme omnipotent ruler of all.