Conditional Probability

The probability of an event occurring given that another event has already occurred.

P(A|B) = P(A and B) / P(B), where P(A|B) is the probability of A given B.

P(A) = P(A|B)P(B) + P(A|¬B)P(¬B), where ¬B is the complement of B.

The probability that both events A and B occur.

Independent events do not affect each other's probabilities, while dependent events do.

P(A and B) = P(A) * P(B) = 0.5 * 0.4 = 0.2.

P(Red) = 3/9 = 1/3.

P(Sports Team | Instrument) = 0.7273.

A way to find a conditional probability when you know the reverse conditional probability: P(A|B) = [P(B|A) * P(A)] / P(B).

P(French | Girl) = 0.4.