5. You and two of your friends compete to see who can answers questions in a quiz game the quickest. Throughout, assume that the time it takes you T and times it takes each of your friends T2, T3 to solve each quiz question are exponentially distributed (i.e., T,~ Exp(A) with A, > 0 for each ie {1,2,3}) and that the collection of random times (T1, T2, T3) are jointly independent. Answer the following. For full credit, you must provide a complete justification of your answer. (a) Assuming that each of your skills are equal (i.e., A, A, for all (i,j) c (1,2,3}), what is the probability that you answer the question first (i.e., T < min{T2, T3})? = (b) Assuming A = .5, A2 = .2, and A = .7, what is the probability you finish first.