Question

In a recent baseball season, Bob hit a home run approximately once every 18.38 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 25th plate appearance of the season? Use Excel to find the probability.

Answer 1

Solution

Probability that Bob hits his first home run before his 25th plate appearance of the season

= 1 - Probability that Bob does not hit his first home run in 24 plate appearances of the season

= 1 – P(X = 0), where X = number of home runs hit in 24 plate appearances of the season.

Now, X ~ B(24, p), where p = 1/18.38 [implied by the given statement, ‘Bob hit a home run approximately once every 18.38 plate appearances.’].

Thus, X ~ B(24, 0.054447) and hence

P(X = 0)

= 0.2609 [Using Excel Function: Statistical BINOMDIST]

So, Probability that Bob hits his first home run before his 25th plate appearance of the season

= 1 – 0.2609

= 0.7391 Answer

DONE