Alice, Benjamin, and Carol each try independently to win a carnival game. If their individual probabilities for success are 1/5, 1/8, and 2/7, respectively, what is the probability that exactly two of the three players will win but one will lose?
Options:
(A) 3/140
(B) 1/280
(C) 27/280
(D) 3/35
(E) 7/56 Let's think first. Stream of consciousness:
user
P = P(A wins, B wins, C loses) + P(A wins, B loses, C wins) + P(A loses, B wins, C wins) = 1/5*1/8*5/7 + 1/5*7/8*2/7 + 4/5*1/8*2/7 = 27/280.
So, the answer is (C).
assistant