When tossed, a certain coin has equal probability of landing on either side. If the coin is tossed 3 times, what is the probability that it will land twice on heads and once on tails?
Options:
(A) 1/16
(B) 1/3
(C) 1/6
(D) 1/2
(E) 1/8
Answer and stream of consciousness: (E)
Stream of consciousness: Must be once on twice and once on tails
1/2*1/2*1/2 = 1/8

Alice, Benjamin, and Carol each try independently to win a carnival game. If their individual probabilities for success are 1/5, 3/8, and 3/7, respectively, what is the probability that exactly two of the three players will win but one will lose?
Options:
(A) 63/280
(B) 1/280
(C) 3/56
(D) 3/35
(E) 7/40
Answer and stream of consciousness: (A)
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*3/8*4/7 + 1/5*5/8*3/7 + 4/5*3/8*3/7 = 63/280.

The speed of a boat in still water is 60kmph and the speed of the current is 20kmph. Find the speed downstream and upstream?
Options:
(A) 80,70 kmph
(B) 87,40 kmph
(C) 80,40 kmph
(D) 70,40 kmph
(E) 80,44 kmph
Answer and stream of consciousness: (C)
Stream of consciousness: Speed downstream = 60 + 20 = 80 kmph
Speed upstream = 60 - 20 = 40 kmph

Two trains are moving at 75 kmph and 70 kmph in opposite directions. Their lengths are 150 m and 100 m respectively. The time they will take to pass each other completely is?
Options:
(A) 6 6/29 sec
(B) 7 1/7 sec
(C) 7 2/2 sec
(D) 8 1/2 sec
(E) 7 1/19 sec
Answer and stream of consciousness:
(A)
Stream of consciousness: 70 + 75 = 145 * 5/18 = 725/18 mps
D = 150 + 100 = 250 m
T = 250 * 18/725 = 180/29 = 6 6/29 sec