Alice, Benjamin, and Carol each try independently to win a carnival game. If their individual probabilities for success are 2/5, 3/8, 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) 3/280
(D) 4/56
(E) 77/280
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P = P(A wins, B wins, C loses) + P(A wins, B loses, C wins) + P(A loses, B wins, C wins) = 2/5*3/8*5/7 + 2/5*5/8*2/7 + 3/5*3/8*2/7 = 77/280. So the answer is: (E).
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Two pipes can fill a tank in 20 and 24 minutes respectively and a waste pipe can empty 3 gallons per minute. All the three pipes working together can fill the tank in 15 minutes. The capacity of the tank is?
Options:
(A) 299
(B) 2767
(C) 120
(D) 287
(E) 261
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Work done by the waste pipe in 1 minute = 1/15 - (1/20 + 1/24) = - 1/40
Volume of 1/40 part = 3 gallons\
Volume of whole = 3 * 40 = 120 gallons. So the answer is: (C).
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A train running at the speed of 60 km/hr crosses a pole in 6 seconds. Find the length of the train.
Options:
(A) 150 m
(B) 145 m
(C) 100 m
(D) 135 m
(E) 155 m
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Speed = 60*(5/18) m/sec = 50/3 m/sec
Length of Train (Distance) = Speed * Time
(50/3) * 6 = 100 meter So the answer is: (C).
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