In this problem. we are interested in finding out the efficiency of a BitTorrent- like P2P file sharing system . Consider two peers Bob and Alice. They join a torrent with M peers in total (including Bob and Alice) that are sharing a file consisting of N chunks. Assume that at a particular time t, the chunks that a peer has are uniformly at random chosen from all N chunks, and no peer has all N chunks. Answer the following questions.
a. What is the probability that Bob has all the chunks that Alice has, given that the numbers of chunks that Bob and Alice have are denoted by nb; and na?
b. Remove part of the conditioning in part a) to find out the probability that Bob has all the chunks that Alice has, given that Alice has na chunks?
c. Suppose that each peer in BitTorrent has 5 neighbors. What is the probability that Bob has data that is of interest to at least one of his five neighbors?