Abaseball 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.

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