Conditional Probability

Conditional probability measures the likelihood of an event occurring given that another event has already occurred. It helps us update probabilities when we have partial information about an outcome.

Example: If 25% of students play sports and study music, and 50% of students play sports, then the probability a sports player also studies music is 25% ÷ 50% = 50%.

The conditional probability of event A given that event B has occurred is defined as:

P(A|B) = P(A ∩ B)/P(B) for P(B) > 0.

This formula represents the proportion of B's probability that also includes A.