$14$ 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 either sits at the table of a friend or at an unoccupied table is none of those present is a friend. Assuming that each of the ${14}\choose{2}$ pairs of people are, independently, friends with probability $0.6,$ find the expected number of occupied tables.

(Hint: One possible approach is to define, for example, $X_3$ to be the random variable whose value is 1 if the third person to arrive sits at an unoccupied table and 0 otherwise.)

Answer: The expected number of occupied tables is