Hi I am having trouble solving a homework problem. It says:
N people arrive separately to a profeesional dinner. Upon arrival each person looks to see if he or she has any friends among those present. That person then either sots at the table of a friend or at an unoccupied table if none of those present is a friend. Assuming that each of the N choose 2 pairs of people are independently friends with probability p find the expected number of occupied tables.
I have X= number of tables and X=X1=X2+...+Xn where each Xi is 1 when they sit at a new table or 0 if they sit with a friend but then I get confused about how to find with what probability they actually sit at a new table
Any ideas would be greatly appreciated

I think I've found the solution to this problem, located at this link:

http://hilbert.math.tufts.edu/~bruceb/Courses/161/Homeworks/HW11sol/

It's the first problem discussed on the page (1. Problem 8, p. 379) - they give a nice detailed explanation of how they arrive at the solution, and the answer is:

expected number of tables = E[Nt] = [ 1 - (1-p)^N ] / p

N=number of guests
p = probability that any pair of people know each other