One interpretation of a baseball player's batting average is as the empirical probability of getting a hit each time the player goes to bat. If a player with a batting average of 0.2260.226 bats 44 times in a game, and each at-bat is an independent event, what is the probability of the player getting at least one hit in the game?

Question

Leonard Herrera

Mathematics

19 October, 08:23

One interpretation of a baseball player's batting average is as the empirical probability of getting a hit each time the player goes to bat. If a player with a batting average of 0.2260.226 bats 44 times in a game, and each at-bat is an independent event, what is the probability of the player getting at least one hit in the game?

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Answers (1)

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Derick Watkins · Answer 1

0.7223

Step-by-step explanation:

Given:

Probability of hitting, p = 0.226

Number of times player bats, n = 44

Now,

P (getting a least one hit) = 1 - P (no hits)

also,

P (not hitting a hit in game) = qⁿ

where,

q = 1 - p

thus,

q = 1 - 0.226 = 0.774

Therefore,

P (not hitting a hit in game) = 0.774⁵ = 0.2777

Hence,

P (getting a least one hit) = 1 - P (no hits)

or

P (getting a least one hit) = 1 - 0.2777

or

P (getting a least one hit) = 0.7223