Problem:
Tina randomly selects two distinct numbers from the set , and Sergio randomly selects a number from the set . The probability that Sergio's number is larger than the sum of the two numbers chosen by Tina is
Answer Choices:
A.
B.
C.
D.
E.
Solution:
There are ten ways for Tina to select a pair of numbers. The sums , and can be obtained in just one way, and the sums , and can each be obtained in two ways. The probability for each of Sergio's choices is . Considering his selections in decreasing order, the total probability of Sergio's choice being greater is
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions