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.

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