TITLE: What does actually probability mean?
QUESTION [8 upvotes]: I am a beginner in quantum information. Reading about it has made me question the definition of probability.

If the probability of an outcome $m$ in an experiment is $p(m)$ then it means that if I perform the experiment $n$ times (  $n \to \infty$ ) then    $p(m)*n$ times I will get the outcome as $m$.

But probability of an outcome by intuition also means how certain we are that we
will get that outcome as a result when we perform the experiment. But according to the first definition  probability of an outcome makes sense when we perform the same experiment a very large number of times. Whereas according to the second definition we are just performing the experiment once and rather express probability as a measure of certainty.

sorry for asking  a trivial question like this.

REPLY [2 votes]: You dip your toe into the waters of controversy with such a question: the quoted definition is the frequentist definition of probability, the second one is called Bayesian, and an excellent way to cause a brawl among statisticians and probabilists is to ask them which they are: see Wikipedia's article for a long summary. There's plenty of other articles around the Internet that talk about this as well, but I thought that this question on Statistics StackExchange was a good explanation as well.
To put this in a physicist's context, it's about as controversial as the interpretation of quantum mechanics (except no statistician is crazy enough to suggest a many-worlds equivalent).