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
