# Question: Repeat the preceding problem when the seating is random but

Repeat the preceding problem when the seating is random but subject to the constraint that the men and women alternate.

Preceding problem

A total of 2n people, consisting of n married couples, are randomly seated (all possible orderings being equally likely) at a round table. Let Ci denote the event that the members of couple i are seated next to each other, i = 1, . . . , n.

(a) Find P(Ci).

(b) For j ≠ i, find P(Cj|Ci).

(c) Approximate the probability, for n large, that there are no married couples who are seated next to each other.

Preceding problem

A total of 2n people, consisting of n married couples, are randomly seated (all possible orderings being equally likely) at a round table. Let Ci denote the event that the members of couple i are seated next to each other, i = 1, . . . , n.

(a) Find P(Ci).

(b) For j ≠ i, find P(Cj|Ci).

(c) Approximate the probability, for n large, that there are no married couples who are seated next to each other.

## Relevant Questions

Suppose in Problem 72 that the two teams are evenly matched and each has probability 12 of winning each game. Find the expected number of games played. Problem 72 Two athletic teams play a series of games; the first team to ...There are three highways in the county. The number of daily accidents that occur on these highways are Poisson random variables with respective parameters .3, .5, and .7. Find the expected number of accidents that will ...Let X be a binomial random variable with parameters (n, p). What value of p maximizes P{X = k}, k = 0, 1, . . . , n? This is an example of a statistical method used to estimate p when a binomial (n, p) random variable is ...Consider a random collection of n individuals. In approximating the probability that no 3 of these individuals share the same birthday, a better Poisson approximation than that obtained in the text (at least for values of n ...Let X be such that P{X = 1} = p = 1 − P{X = −1} Find c ≠ 1 such that E[cX] = 1.Post your question