2

Exercise 2. (15 points) A Pair of dice is rolled until a sum of either 2 or 5 appears. The aim is to calculate the probability that a 2 occurs first. Let En denote the event that a 2 occurs on the nth roll and no 2 or 5 occurs in the first n - 1 rolls. (a) Show that En are mutaully disjoints and compute P(En) (b) Show that Un En = {event 2 occurs first } ; and compute P(event 2 occurs first) (c) Compute P(event 2 occurs first)