You and a friend are playing a best-of-three series (first to win 2 games wins the series). You are a stronger player and have a 0.68 chance of winning each game. Both you and your friend play better after winning a game. If you win a game, your chance of winning the next game is 0.81. If your friend wins a game, the chance they win the next game is 0.73. What is the probability you win the series

Answer and Step-by-step explanation:

Given that probability of you winning each game = 0.68

And probability of you winning next game = 0.81

Your friend's chance of winning/you losing would be = 1-0.68= 0.32

also his chance of winning next game = 0.73

To find probability that you would win the series given that you need to win two games to win the series

= probability that you win first game and second game+ probability that you win first game, lose second game and win third game + probability that you lose first game, win second game and win third game

= 0.68*0.81+0.68*0.32*0.68+0.32*0.68*0.81

=0.8750

Therefore probability that you would win the series = 0.8750

Note: here we found the probability of winning by adding(or) up the three possible combinations that would result in a win

a negative exponent is translated as follows:

so, we have