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 * 0.5^{6} * 0.5^{6} =
0.2256

b) P(X = 9) = 12C9 * 0.5^{9} * 0.5^{3} =
0.0537

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

= 12C9 * 0.5^{9} * 0.5^{3} + 12C10 *
0.5^{10} * 0.5^{2} + 12C11 * 0.5^{11} *
0.5^{1} + 12C12 * 0.5^{12} * 0.5^{0}

= 0.0730

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