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.

The probability of event A occurring given that event B has occurred.

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

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

It states that the total probability of an event can be found by considering all possible ways that event can occur.

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

P(A and B) = P(A) * P(B).

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

The complement of an event A is the event that A does not occur, denoted as ¬A.