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Statistics / A First Course in Probability 9 / Chapter 4 / Problem 22P

A First Course in Probability | 9th Edition | ISBN: 9780321794772 | Authors: Sheldon Ross

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Suppose that two teams play a series of games that ends

Chapter 4, Problem 22P

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QUESTION:

Problem 22P

Suppose that two teams play a series of games that ends when one of them has won i games. Suppose that each game played is, independently, won by team A with probability p. Find the expected number of games that are played when (a) i = 2 and (b) i = 3. Also, show in both cases that this number is maximized when p = .

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QUESTION:

Problem 22P

Suppose that two teams play a series of games that ends when one of them has won i games. Suppose that each game played is, independently, won by team A with probability p. Find the expected number of games that are played when (a) i = 2 and (b) i = 3. Also, show in both cases that this number is maximized when p = .

ANSWER:

Solution:

Step 1 of 3:

Let two teams play a series of games. The game will end if one of them has won i games.

Team A won the game with probability p.

We have to find the expected number of games that are played if,

i=2,
i=3.

We need show that in both cases this number maximized when p= $\frac{1}{2}$ .

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