Corrupted by their power, some of the judges in a popular reality show have been taking bribes from many of the contestants. Out of 5 total judges, 3 are corrupt. The identity of corrupt judges is known to the contestants. Each episode, a given contestant is either allowed to stay on the show or is kicked off. Let / be the number of judges a contestant has been bribing. If the contestant has been bribing the judges they will be allowed to stay with a probability given by max(1/5, N/3) . Note that N = {0, 1, 2, 3}. Suppose that 1/16 of the contestants have been bribing only one judge, 1/8 of the contestants have been bribing only two judges, and 1/4 of the contestants have been bribing all three of the corrupt judges. The same contestants bribe the same set of judges in both rounds, i.e., if a contestant bribes / judges in the first round, she will bribe the same set of N judges in the second round too (and vice versa). 1. If you pick a random contestant who was allowed to stay during the first episode, what is the probability that she was bribing the judges? (3) 2. If you pick a random contestant, what is the probability that she is allowed to stay during both of the first two episodes? (3) 3. If you pick random contestant who was allowed to stay during the first episode, what is the probability that she gets kicked off during the second episode? (4)