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11 September, 10:48

A baseball player's batting average is 250. Find each of the following probabilities that he will get hits. a. Exactly 2 hits in 4 times at bat. b. At least one hit in 4 times at bat.

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  1. 11 September, 11:06
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    Answer:P (x = 2) = 0.21

    P (x ≥ 1) = 0.264

    Step-by-step explanation:

    We would apply the binomial distribution formula which is expressed as

    P (x = r) = nCr * q^ (n - r) * p^r

    Where

    p = probability of success.

    q = probability of failure = 1 - p

    n = number of samples

    From the information given,

    p = 0.25

    q = 1 - 0.25 = 0.75

    n = 4

    a) we want to determine the probability that he gets exactly 2 hits in 4 times at bat. It is expressed as P (x = 2)

    P (x = 2) = 4C2 * 0.75^ (4 - 2) * 0.25^2 = 0.21

    b) we want to determine the probability that he gets At least one hit in 4 times at bat. It is expressed as P (x ≥ 1) = 1 - P (x ≤ 1)

    1 - P (x ≤ 1) = P (x = 0) + P (x = 1)

    P (x = 0) = 4C0 * 0.75^ (4 - 0) * 0.25^0 = 0. 316

    P (x = 1) = 4C1 * 0.75^ (4 - 1) * 0.25^1 = 0.42

    P (x ≤ 1) = 0. 316 + 0.42 = 0.736

    P (x ≥ 1) = 1 - 0.736 = 0.264
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