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4. (25 points) An Oympic archer is able to hit the bull's-eye 80% of the time. Assume each slot is independent of the others. If she shoots 6 arrows, Whatls the probability of each of the following results? (a) Her rst bull's-eye comes on the third arrow. (b) She misses the bull's-eye at least once. (c) Her rst bull's-eye comes on the fourth or fth arrow. (d) She gets exactly 4 bull's-eyes. (e) What's the probability that she gets at least 4 bull's-eyes? What's the probability that she gets at most 4 bull's-eyes? 5. (25 points) Suppose the archer the above question shoots 10 arrows. (a) Find the mean and standard deviation of the number of bull's-eyes she may get. (b) What's the probability that she never misses? (c) What's the probability that there are no more than S bull's-eyes\"? (d) What's the probability that there are exactly 8 bull's-eyes? (e) What's the probability that she hits the bull's-eye more often than she misses