Question

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?

Answer 1

Answer:

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