Question

The probability that Hank Aaron hits a hone run on any given at bar is 0.14, and each at bat is independent

Part A: What is the probability that the next home run will be on his fifth at bat?

Part B: What is the expected number of at bats until the next home run?

Answer 1

Given the probability that Hank Aaron hits a home run on any given at bat is p=0.14

Let X be the hits required for the next hit home run.

Therefore,

The pmf of X is

for x=1,2,3,...

a) The probability that the next home run will be on his fifth at bat is given by:

Thus probability that the next home run will be on his fifth at bat is

b) The expected number of at bats until the next home run is given by:

       ### Expected value of geometric random variable is 1/p

Hence, the expected number of at bats until the next home run is