Q: 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
A: OK... Stream of consciousness: 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.
The answer is (C).

Q: If f(x) = x^3/(x^5 - 1), what is f(1/x) in terms of f(x)?
Options:
(A) -f(x) 
(B) 1/f(x) 
(C) 2/f(x) 
(D) 3/f(x) 
(E) f(x) 
A: OK... Stream of consciousness: If x = 2 then f(x) = 8/31 and f(1/x) = -8/31 which is equal to -f(x)
The answer is (A).

Q: The volume of a certain substance is always directly proportional to its weight. If 48 cubic inches of the substance weigh 114 ounces, what is the volume, in cubic inches, of 63 ounces of this substance?
Options:
(A) 27
(B) 26
(C) 42
(D) 64
(E) 147
A: OK... Stream of consciousness: 112 ounces of a substance has a volume of 48 cubic inches
63 ounces of a substance has a volume of (48/114)*63 = 26 cubic inches
The answer is (B).

Q: What is the median from the below series
90, 92, 93, 88, 95, 88, 97, 87, and 98
Options:
(A) 85
(B) 89
(C) 92
(D) 98
(E) 100
A:

Show your work and conclude with the exact phrasing "Therefore, the final answer is [answer]." where [answer] is just the final number or expression that solves the problem.
user
OK... Stream of consciousness: Ordering the data from least to greatest, we get:
87, 88, 88, 90, 92, 93, 95, 96, 98
The median score is 92.
The answer is (C).