Question

The probability that Babe Ruth hits a home run on any given at-bat is 0.12, 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)​

Answer 1

A) 0.072 = 7.2%

B) 8.3333 at-bats (8 to 9 at-bats)

Explanation:

A)

If the chance of hitting a home run is 0.12, the chance of not hitting a home run is 1 - 0.12 = 0.88.

To find the probability of the next home run being in the fifth strike, we need the four other strikes to not be a home run, so the probability is:

P = (0.88)^4 * 0.12 = 0.072 = 7.2%

B)

To find the expected number of at-bats until the next home run, we just need to divide 100% by the probability of hitting a home run (0.12 = 12%):

100/12 = 8.3333

So the expected number is 8 to 9 at-bats