Suppose you and your friend are going to a beach party. Two of you are bringing a cooler box with sandwiches. Your cooler box contains 8 ham sandwiches and 5 cheese sandwiches. Your friends cooler box contains 7 ham sandwiches and 7 cheese sandwiches. At the beach, someone takes a sandwich at random, and it's a ham sandwich. What is the probability that it came from your cooler box? An urn contains four balls, numbered 1, 2, 3 and 4. Two balls are drawn from the urn with replacement. The order the balls were chosen is important in this experiment. (a) List the sample space of the experiment. (b) Find the probability of the following events: I. Event that the sum of the balls is equal to five. II. Event that the first ball chosen is even and the second ball chosen is odd. (c) Are the events (I) and (II) mutually exclusive? Motivate your answer! (d) Are the events (I) and (II) independent? Motivate your answer! In a game, a participant is given three attempts to hit a ball. On each try, she either scores a hit (H), or a miss (M). The game requires that the player must alternate which hand she uses in successive attempts. That is, if she makes her first attempt with her right hand, she must use her left hand for the second attempt and her right hand for the third. Her chance of scoring a hit with her right hand is 0.9 and with her left hand is 0.2. Assume that her attempts are independent and that she wins the game if she scores at least two hits in a row (e.g. HHM). If she makes her first attempt with her right hand what is the probability that she wins the game?

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