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Probability and Statistics for Engineers and Scientists | 4th Edition | ISBN: 9781111827045 | Authors: Anthony J. Hayter
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In a typical sports playoff series, two teams play a

Chapter 3, Problem 3.8.6

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QUESTION:

In a typical sports playoff series, two teams play a sequence of games until one team, the eventual winner, has won four games. Suppose that in each game team A beats team B with a probability of 0.55, and that the results of different games are independent.

(a) Explain how the negative binomial distribution can be used to analyze this problem.

(b) What is the probability that team A wins the series in game seven?

(c) What is the probability that team A wins the series in game six?

(d) What is the probability that the series is over after game five?

(e) What is the probability that team A wins the series?

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QUESTION:

In a typical sports playoff series, two teams play a sequence of games until one team, the eventual winner, has won four games. Suppose that in each game team A beats team B with a probability of 0.55, and that the results of different games are independent.

(a) Explain how the negative binomial distribution can be used to analyze this problem.

(b) What is the probability that team A wins the series in game seven?

(c) What is the probability that team A wins the series in game six?

(d) What is the probability that the series is over after game five?

(e) What is the probability that team A wins the series?

ANSWER:

Step 1 of 7

The negative binomial distribution is a discrete probability distribution that models the number of successes in a sequence of trials until a certain number of failures occur. It is often used to model situations such as the number of coin flips needed to get 5 heads or the number of customers that need to be served before 3 leave without being served.

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