# Question: N people arrive separately to a professional dinner Upon arrival

N people arrive separately to a professional dinner. Upon arrival, each person looks to see if he or she has any friends among those present. That person then sits either at the table of a friend or at an unoccupied table if none of those present is a friend. Assuming that each of the

pairs of people is, independently, a pair of friends with probability p, find the expected number of occupied tables.

Let Xi equal 1 or 0, depending on whether the ith arrival sits at a previously unoccupied table.

pairs of people is, independently, a pair of friends with probability p, find the expected number of occupied tables.

Let Xi equal 1 or 0, depending on whether the ith arrival sits at a previously unoccupied table.

## Answer to relevant Questions

A total of n balls, numbered 1 through n, are put into n urns, also numbered 1 through n in such a way that ball i is equally likely to go into any of the urns 1, 2, . . . , i. Find (a) The expected number of urns that are ...Suppose that each of the elements of S = {1, 2, . . . , n} is to be colored either red or blue. Show that if A1, . . . ,Ar are subsets of S, there is a way of doing the coloring so that at most of these subsets have all ...Show that Y = a + bX, then An urn contains a white and b black balls. After a ball is drawn, it is returned to the urn if it is white; but if it is black, it is replaced by a white ball from another urn. Let Mn denote the expected number of white ...An insurance company has 10,000 automobile policyholders. The expected yearly claim per policyholder is $240, with a standard deviation of $800. Approximate the probability that the total yearly claim exceeds $2.7 million.Post your question