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 0.6, 0.7, 0.8 and 0.9, respectively, when playing against members Carrie, David, Paul and Rose. Wheather she wins or loses is independent from one game to the next.

a. What is the probability that Laurie will lose when she play against Rose?

b. If Laurie plays one game against each player, what is the probability that she does not lose any games?

c. If Laurie plays one game against each player, what is the probability that she loses at least once?

Explanation / Answer

a) Probability that Laurie will lose when she play against Rose = 1 - 0.9 = 0.1

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

c) P( she loses at least once) = 1 - P(she does not lose any games) = 1 - 0.3024 = 0.6976

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