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A professional soccer player succeeds in scoring a goal on 84% of his penalty kicks. Assume...

A professional soccer player succeeds in scoring a goal on 84% of his penalty kicks. Assume that the success of each kick is independent.

(a) In a series of games, what is the probability that the first time he fails to score a goal is on his fifth penalty kick?

(b) What is the probability that he scores on 5 or fewer of his next 10 penalty kicks?

(c) Suppose that our soccer player is out of action with an injury for several weeks. When he returns, he only scores on 5 of his next 10 penalty kicks. Is this evidence that his success rate is now less than 84%? Explain.

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