Conditional probability

Conditional probability is one of the most important concepts in probability theory. In theory it is the probability that a given event occurs given the knowledge of some partial information about the results of the experiment.

For example, in a die tossing experiment, the probability of getting either 6 faces of the fair die is 1/6 (evenly split). If we know that the final result of the experiment is even (i.e either 2, 4 or 6), the conditional probabilities for all 6 faces of the die change. The probability of obtaining a 1, 3 or 5 will go down to 0, while the probability of obtaining a 2, 3 or 6 will go up to 2/6 (or 1/3). These new probabilities are conditioned on the fact that our result is even, and known as conditional probablities.