Question

A computer chess game and a human chess champion are evenly matched. They play twelve games. Find probabilities for the following events. (Round all answers to four decimal places.) (a) They each win six games. P = (b) The human chess champion wins nine games. P = (c) The human chess champion wins at least nine games. P =

Answer 1

p = 0.5

n = 12

This is a binomial distirbution

P(X = x) = 12Cx * 0.5^x * (1 - 0.5)^12-x

a) P(X = 6) = 12C6 * 0.5⁶ * 0.5⁶ = 0.2256

b) P(X = 9) = 12C9 * 0.5⁹ * 0.5³ = 0.0537

c) P(X > 9) = P(X = 9) + P(X = 10) + P(X = 11) + P(X = 12)

                  = 12C9 * 0.5⁹ * 0.5³ + 12C10 * 0.5¹⁰ * 0.5² + 12C11 * 0.5¹¹ * 0.5¹ + 12C12 * 0.5¹² * 0.5⁰

                  = 0.0730