Your favorite team is in the final playoffs. You have assigned a probability of 60% that they will win the championship. Past records indicate that when teams win the championship, they win the first game of the series 70% of the time. When they lose the series, they win the first game 25% of the time. The first game is over; your team has lost. What is the probability that they will win the series?
The probabilities are given below: P1-win the 1st game and win the series = 0.7*0.6=0.42; P2-win the 1st and lose the series = 0.25*(1-0.6) = 0.1; P3-lose the 1st game and win the series = 0.6-0.42=0.18; P4-lose the 1st game and lose the series = 0.4-0.1=0.3; P(win the series|lose the 1st game)= 0.18/0.48=0.375, where 0.48=0.18+0.3 is the probability& of losing the 1st game;