# Question: A total of 2n people consisting of n married couples

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.

(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.

## Answer to relevant Questions

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 ...Suppose that a batch of 100 items contains 6 that are defective and 94 that are not defective. If X is the number of defective items in a randomly drawn sample of 10 items from the batch, find (a) P{X = 0} and (b) P{X > 2}. There are n components lined up in a linear arrangement. Suppose that each component independently functions with probability p. What is the probability that no 2 neighboring components are both nonfunctional? An urn contains 2n balls, of which 2 are numbered 1, 2 are numbered 2, . . . , and 2 are numbered n. Balls are successively withdrawn 2 at a time without replacement. Let T denote the first selection in which the balls ...Suppose the possible values of X are {xi}, the possible values of Y are {yj}, and the possible values of X + Y are {zk}. Let Ak denote the set of all pairs of indices (i, j) such that xi + yj = zk; that is, Ak = {(i, j): xi ...Post your question