2012-05-17 09:00:59

If x is chosen at random from the set {2, 3, 5, 7, 8} and y is chosen at random from the set {1, 3, 5, 7, 9}, what is the probability that xy > 27?

(A) 1/5
(B) 7/25
(C) 8/25
(D) 18/25
(E) 21/25

The correct answer is C

Explanation: Probability is the number of desired outcomes divided by the number of possible outcomes. The number of possible outcomes here is 25 (from 5 numbers chosen from set x multiplied by 5 numbers chosen from set y), while the number of desired outcomes can be found by seeing which combinations of numbers from x and y will multiply together to be greater than 27. Any number from set y will not multiply with 2 or 3 (from x) to be greater than 27. However, 5 (from x) will multiply by 7 and 9 to be greater than 27; as will 7 (from x) and 5, 7, or 9 (from y); and 8 (from x) and 5, 7, or 9 (from y). This means 8 combinations of numbers will work, meaning the probability in question is 8/25, or choice C.