Kevin plays chess with Aaron, the probability Kevin wins is 0.75. Aaron and Kevin play 25 games, what is the probability that Kevin wins exactly 15 times?

Question

When Kevin plays chess with Aaron, the probability that Kevin wins is 0.75. Of Aaron and Kevin play 25 games, what is the probability that Kevin wins exactly 15 times?

Answer 1

Out of 25 games, we can find the number of ways that Kevin wins exactly 15:

This number is 25 C 15 (25 choose 15) = 3268760.

The probability that Kevin wins 15 (and thus loses exactly 10) is:

(0.75)^15 * (0.25)^10 * 3268760 = 0.0417.