Question

In a recent baseball season, Bob hit a home run approximately once every 16.65 plate appearances. Assume that this probability did not change going into the next season. What is the probability that Bob hits his first home run before his 21st plate appearance of the season? Use a TI-83, TI-83 Plus, or TI-84 calculator to find the probability, rounding to three decimal places.

Answer 1

The probability of Bob hitting his first home run before his 21st plate appearance is calculated by using the geometric cumulative distribution function on a TI-83/TI-84 and subtracting the result from 1, then rounding to three decimal places.

Step-by-step explanation:

The probability that Bob hits his first home run before his 21st plate appearance can be calculated using the geometric distribution, which deals with the number of Bernoulli trials needed for a success.

Using a TI-83 or TI-84 series calculator, we would calculate 1 minus the probability of Bob not hitting a home run in his first 20 plate appearances. The probability of not hitting a home run each time he's at bat is 1 - 1/16.65.

To find the cumulative probability of Bob not hitting a home run in 20 plate appearances, we use the geometric cumulative distribution function (geometcdf): geometcdf(16.65,20). Then we subtract this value from 1 to get the probability of a home run before the 21st appearance. Assuming the value from the calculator is P, the answer will be rounded to three decimal places as 1-P.