Find the missing factor. write your answer inexponential form.9^2=9^4×

a) Probability that the next home run will be on his fifth at-bat = 0.0797

b) The expected number of at-bats until the next home run = 6.25

Step-by-step explanation:

Let's take X as the number of hits needed for the next home run.

Given, P = 0.16

X~ GEOM. (P = 0.16)

For the probability main function of X, we have

P(X = x) = (1 - P)ˣ⁻¹ p; x = 0, 1, 2, 3....

a) For the probability that the next home run will be on his fifth at-bat.

P(X = 5)

(1 - 0.16)⁵⁻¹ (0.16)

= 0.07965942 ≈ 0.797

Probability that the next home run will be on his fifth at-bat = 0.0797

b) The expected number of at-bats until the next home run?

Let's use:

= 6.25

The expected number of at-bats until the next home run = 6.25