*This problem discusses why and how a batting average differs from the probability of a hit.*

**Question:**The likelihood a batter realizes an official at bat each time he comes to the plate is 4/5. His batting average is 0.300. What is the probability that he gets a hit in each plate appearance?

**Answer**: An appearance at the plate does not always result in an official at bat because a person can be walked, hit by a pitch, or successfully implement a sacrifice. A hit can only occur when the batter has an official at bat. The batting average is the conditional probability of a hit given that a plate appearance results in an official at bat.

Intuitively, the probability of a hit for all plate appearances is the weighted average of the probability of a hit given that the plate appearance ends up in an at bat and the probability of a hit given that the plate appearance does not result in an at bat. This is Baye’s law.

P(Hit)= P(Hit/At bat)x(P(At bat) +P(Hit/No at bat) x P(No at bat)

In the current problem:

P(Hit)=(0.300)x(4/5)+0x((1/5)

=0.240

**Author's Note**:

Please consider my book on Kindle:

The book is a bit dated and needs improvement. It has some useful and interesting problems. I am working on a second edition.

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