You are trying to maintain radio communication while an adversary is trying to jam your communication. You are using 2 out of 5 available radio channels. To organize his random search, the adversary starts with a deck of 5 cards, labeled 1 through 5, and shuffles it. In each time slot, he picks up a card from the deck and scans the channel corresponding to the label of the card. He then puts the card in the discard pile so that he doesn't scan the same channel again. If the adversary picks one of your used channels, he will find out when he scans it, and he will jam it. We also number time slots 1, 2, 3, ... What is the chance that by the end of time slot k, the adversary has found none of the channels you are using? In other words, if we let the random variable X be the time slot number in which the adversary makes his first discovery of one of your channels, we are looking for P(X >k). Obviously, by slots 4 and 5 the adversary will have to have found one or more of your channels, so P(X >4)=P(X>5) = 0. Therefore you can give probabilities for P(X > k) in the k= 1, 2, and 3 cases. HINTS: . For k=1: think about what fraction of channels aren't being used since if the adversary picks one of those he will fail to find a used channel in slot 1 and hence X> 1. . For k=2: For the event X>2 to be true we require both of the following: i) The adversary finds an unused channel in slot 1. ii) The adversary finds an unused channel in slot 2 after having found an unused channel in slot 1. k=1 K=2 k=3 k=4 k=5 P(X>k) ? .V .V