?Cold Streaks Players in sports are said to have “hot streaks” and “cold streaks.” For example, a batter in baseball might be considered to be in a slu

Chapter 5, Problem 24

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Cold Streaks Players in sports are said to have “hot streaks” and “cold streaks.” For example, a batter in baseball might be considered to be in a slump, or cold streak, if he has made 10 outs in 10 consecutive at-bats. Suppose that a hitter successfully reaches base 30% of the time he comes to the plate.

(a) Find and interpret the probability that the hitter makes 10 outs in 10 consecutive at-bats, assuming that at-bats are independent events. Hint: The hitter makes an out 70% of the time.

(b) Are cold streaks unusual?

(c) Find the probability the hitter makes five consecutive outs and then reaches base safely.

(d) Discuss the assumption of independence in consecutive at-bats.

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