Question

Two tennis players, A and B, are playing in a tournament; the first person to win 3 sets is declared the winner of the match (best of 5. no ties allowed) Assume that A is stronger and wins each set with probability of 0.6 and the outcome of each set is independent of other sets.

a.) What is the probability player A will win the match? (With explanation)

b.) Let A and B be events such that P(A) = 0.45, P(B) = 0.3, and P(A U B) = 0.6. Find P(A|B) and P(B|A). (With explanation) Thanks!!!!!!

Answer 1

a) P(A will win the match) = P(A wins first 3 sets) + P(A wins 2 seta out of first 3 and win fourth one) + P(A wins 2 out of first 4 and win fifth one)

                                          = 0.6³ + 3C2 * 0.6² * 0.4¹ * 0.6 + 4C2 * 0.6² * 0.4² * 0.6

                                          = 0.6826

b) P(A U B) = P(A) + P(B) - P(A and B)

or, 0.6 = 0.45 + 0.3 - P(A and B)

or, P(A and B) = 0.15

P(A | B) = P(A and B) / P(B) = 0.15 / 0.3 = 0.5

P(B | A) = P(A and B) / P(A) = 0.15 / 0.45 = 0.33