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A and B play a scries of games. Each game is independently
Chapter 3, Problem 78P(choose chapter or problem)
Problem 78P
A and B play a scries of games. Each game is independently won by A with probability p and by B with probability 1 − p. They stop when the total number of wins of one of the players is two greater than that of the other player. The player with the greater number of total wins is declared the winner of the series.
(a) Find the probability that a total of 4 games are played.
(b) Find the probability that A is the winner of the series.
Questions & Answers
QUESTION:
Problem 78P
A and B play a scries of games. Each game is independently won by A with probability p and by B with probability 1 − p. They stop when the total number of wins of one of the players is two greater than that of the other player. The player with the greater number of total wins is declared the winner of the series.
(a) Find the probability that a total of 4 games are played.
(b) Find the probability that A is the winner of the series.
ANSWER:
Step 1 of 3
It is given that A and B players play a series of game with p being the probability of winning a game by player A and (1-p) being the probability of winning the game by player B.
They stop playing when one player wins two games more than the other player and the player with greater number of games own is declared as the winner of the series.
Using this we need to find the required values.