Question

A and B play a series of games with A winning each game with probability $p$. The overall winner is the first player to have won two more games than the other. (a) Find the probability that $\mathrm{A}$ is the overall winner. (b) Find the expected number of games played.

          A and B play a series of games with A winning each game with probability $p$. The overall winner is the first player to have won two more games than the other.
(a) Find the probability that $\mathrm{A}$ is the overall winner.
(b) Find the expected number of games played.

Added by David C.

Probability with Applications in Engineering, Science, and Technology

Matthew A. Carlton • Jay L. Devore 2nd Edition

Instant Answer

Solved by Expert Madhur L

02/16/2023

Step 1

We have the following possibilities: - If A is ahead by 2 games, then A is the overall winner. So, $P_2 = 1$. - If A is ahead by 1 game, then either A wins the next game with probability p (and A becomes the overall winner), or B wins the next game with Show more…

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A and B play a series of games with A winning each game with probability $p$. The overall winner is the first player to have won two more games than the other. (a) Find the probability that $\mathrm{A}$ is the overall winner. (b) Find the expected number of games played.