Conditional Probability

The probability of an event occurring given that another event has already occurred. It is denoted as P(A|B), which reads 'the probability of A given B'.

P(A|B) = P(A and B) / P(B), where P(A and B) is the joint probability of both events occurring.

The probability that a student is female given that they are a part-time student.

It implies that there is a 67% chance of event A occurring given that event B has occurred.

P(A|B) = [P(B|A) * P(A)] / P(B), used to find conditional probabilities.

Venn Diagrams visually represent the relationships between different events, helping to calculate probabilities of unions and intersections.

The probability that a student is full-time given that they are male.

There is a 2 out of 7 chance that a student is wearing sandals given that they are wearing pants.

If two events A and B are independent, then P(A|B) = P(A). The occurrence of B does not affect the probability of A.

It means that event A will definitely occur if event B has occurred.