Reference no: EM131796637

A dormitory has n students, all of whom like to gossip. One of the students hears a rumor, and tells it to one of the other n -1 students picked at random. Subsequently, each student who hears the rumor tells it to a student picked at random from the dormitory (excluding, of course, himself/ herself and the person from whom he/ she heard the rumor). Let p_r be the probability that the rumor is told r times without coming back to a student who has already heard it from a dormitory mate. So p1 = p2 = 1, and p_n =  0.

a) Find a formula for p_r for r between 3 and n - 1.

b) Estimate this probability for n = 300 and r = 30.