16. A dormitory has n students, all of whom like to gossip. One of the students hears a rumor, and tells it to one of th

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16 A Dormitory Has N Students All Of Whom Like To Gossip One Of The Students Hears A Rumor And Tells It To One Of Th 1 (59.43 KiB) Viewed 245 times

For part b, Using exponential approximation
16. 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 pr 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 pı = P2 = 1, and Pn = 0. a) Find a formula for pr for r between 3 and n - 1. b) Estimate this probability for n = 300 and r = 30.