Suppose that when a 7.0 earthquake hits, it will destroy each highway independently with probability p = 0:3. A town becomes isolated if it loses connections to all the other towns. Let X denote the number of isolated towns when a 7.0 earthquake hits. For instance, in the example on the right, town 3 becomes isolated, but not the other 4 towns, so X = 1.
(a) What are the possible values of X?
(b) What is the probability that X assumes its largest possible value?
(c) Find E[X]