A chess club has 5 players with unequal skill. Laurie is the best player. The pr

Question

A chess club has 5 players with unequal skill. Laurie is the best player. The probability that she will win depends on who her opponent is, with probabilities of winning of .6, .7, .8 and .9, respectively, when playing against members Carrie, David, Paul and Rose. Whether she wins or loses is independent from one game to the next. a. What is the probability that Laurie will lose when she plays against Rose? If Laurie plays one game against each player, what is the probability that she does not lose any games? If Laurie plays one game against each player, what is the probability that she loses at least once?

Explanation / Answer

a) P(Laurie will lose when she play against Rose) = 1 - 0.9 = 0.1

b) P(she does not lose any game) = 0.6x0.7x0.8x0.9 = 0.3024

c) P(she lose at least once) = 1 - P(she does not lose any game)

= 1 - 0.3024

= 0.6976

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