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According to historical data, the probability that a team scores in an inning

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According to historical data, the probability that a team scores in an inning (actually half an inning, call it a batting inning,) is .273 and this number is independent from inning to inning and from team to team. A baseball game has 18 batting innings. Let X equal the number of batting innings in a game where 0 runs are scored. Let Y equal the number of batting innings until the first run is scored.

a. What is the probability X=18?

b. What is the variance of X?

c. What is the probability that X > 13?

d. What is the probability that X > 14?

e. What is the probability that Y = 6?

f. What is the probability the teams score in the 1st 4 consecutive batting innings?

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