Chapter 2: Conditional Probability
Conditional Probability Definition, Formula and Solved Examples Definition of Conditional Probability Let A and B be two events in a sample space S , where P(B) > 0. The conditional probability of A given that B has already occurred is denoted by P(A | B) and is defined as P(A | B) = P(A ∩ B) / P(B) The occurrence of event B reduces the original sample space to B. We then determine what proportion of B also belongs to A. Sample Space S A B A ∩ B Figure 1: Conditional probability considers the part of A lying inside B. The multiplication rule follows directly: P(A ∩ B) = P(A | B) P(B) Similarly, P(A ∩ B) = P(B | A) P(A) Example 1: Drawing a Card A card is drawn randomly from a standard deck of 52 cards. Given that the selected card is a face card, find the probability that it is a king. K ♠ Q ♥ J ♦ 12 Face Cards Figure 2: Kings, Queens and Jacks form the 12 ...