4. A total of 2n people, consisting of n married couples, are randomlydivided into n pairs. Arbitrarily number the women, and let W,denote theevent that woman i is paired with her husband.(a) Find Pr(W;).(b) For i + j, find Pr(WĄW; ).(c) When n is large, approximate the probability that exactly one wife ispaired with her husband.(d) If each pairing must consist of a man and a woman, what does theproblem reduce to?

4. A total of 2n people, consisting of n married couples, are randomly divided into n pairs. Arbitrarily number the women, and let W,denote the event that woman i is paired with her husband. (a) Find Pr(W;). (b) For i + j, find Pr(W|W;). (c) When n is large, approximate the probability that exactly one wife is paired with her husband. (d) If each pairing must consist of a man and a woman, what does the problem reduce to?

4. A total of 2n people, consisting of n married couples, are randomly divided into n pairs. Arbitrarily number the women, and let W,denote the event that woman i is paired with her husband. (a) Find Pr(W;). (b) For i + j, find Pr(W|W;). (c) When n is large, approximate the probability that exactly one wife is paired with her husband. (d) If each pairing must consist of a man and a woman, what does the problem reduce to?

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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