q: In Hockey game, one player throws two fair, six-sided die at the same time. If the player receives at least a five or a one on either die, that player wins. What is the probability that a player wins after playing the game once?
Options:
(A) 1/3
(B) 4/9
(C) 5/9
(D) 2/3
(E) 3/4
a: OK... In Hockey game, Probably the easiest approach would be to find the probability of the opposite event and subtract it from 1:
P(win) = 1- P(not win) = 1 - 4/6*4/6 = 5/9.
The answer is (C).

q: What is the probability that Company G's advertisement will be one of the first two be shown during the first commercial break?
Options:
(A)  1/ 225
(B)  1 / 30
(C)  1 /15
(D)  2 / 15
(E)  4 /15
a: OK... G 1/15 + (14/15) * 1/14 = 2/15
The answer is (D).

q: 5,9,19,31,51,__
Options:
(A) 84
(B) 80
(C) 81
(D) 82
(E) 83
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... (9+5) +5 = 19
(16+9) +6 = 31
(28+16)+7 = 51
(48+28)+8 = 84
The answer is (A).