Problem 5: A tournament is being run between two teams, A and B. This is a 2- to
ID: 3314762 • Letter: P
Question
Problem 5: A tournament is being run between two teams, A and B. This is a 2- tournament meaning that the first team to win 2 games is the tournament winner (sometimes called a best-two-out-of-three tournament). For the first game, the probability of A winning is PA wins]-1/3. For all ensuing games the probability that team A wins is PA wins- 1/3 unless team A lost on the previous round in which case PA wins-3/5. Part 5a: What is the probability that the tournament requires the full three games to decide a winner? Part 5b: The tournament concludes after two games. What is the probability that A won?Explanation / Answer
5a)probability that touranment require full 3 games =P(in first two games A won once)
=P(A wins first and lost second+Alost first and wins second) =(1/3)*(2/3)+(2/3)*(2/3)=6/9=2/3
5b) proabability that tournament conclude in two games =P(A wins both +A loses both)=(1/3)*(1/3)+(2/3)*(1/3)=3/9=1/3
hence probability A won given tournament ends in 2 games =P(A won both)/P( tournament ends in 2 games)
=(1/3)*(1/3)/(1/3) =1/3