(04.03 MC)
The probability that Barry Bonds hits a home run on any given at-bat is 0.16, and each at-bat is independent.
Part A: What is the probability that the next home run will be on his fifth at-bat? (5 points)
Part B: What is the expected number of at-bats until the next home run? (5 points)

Check the explanation

Step-by-step explanation:

The given problem can be modeled into a geometric distribution as follows.

Suppose, X be the number of at-bats required to get a home run. As each at-bat is independent.

A.

Required probability is given by

P(X=5)=(1-0.16)^{5-1}0.16=0.07965942

B.

We have to calculate E(X).

Subtracting later from earlier we get,

So, expected number of at-bats until home run = 1/0.16 = 6.25

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

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step-by-step explanation: