A very expensive random number generator

Probability Level 5

Recently, Derek Jeter played in the $1,000^\text{th}$ game in which he has had two or more hits. If hits are randomly distributed, how many multi-hit games would we expect him to have by this point in his career?

Assumptions and details

He has played in 2,681 career games.
He has 4 at bats in each game he plays.
His batting average is 0.311 (number of hits divided by number of at bats).
You may want to read Baseball rules if you are not familiar with it.

The answer is 985.935.

1 solution

Patrick Corn
Jul 11, 2014

Let $p = 0.311$ . The probability of an 0-for-4 game is $(1-p)^4$ . The probability of a 1-for-4 game is $4p(1-p)^3$ . So he should have $2681(1-(1-p)^4-4p(1-p)^3) = 985.93$ multihit games.

I can't understand where did you get that probability

Hafizh Ahsan Permana - 6 years, 11 months ago

I interpreted the problem to mean that he had exactly 3335 hits across 10724 at-bats and that they were randomly distributed, and got an average of 986 multi-hit games through Monte Carlo methods. I guess the number of at bats is so large that it doesn't make statistical difference which method you use.

Daniel Ploch - 6 years, 10 months ago

A very expensive random number generator

The answer is 985.935.

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