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:
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B.
C.
D.
E.
Solution:
There are ten ways for Tina to select a pair of numbers. The sums 9,8 , 4 , and 3 can be obtained in just one way, and the sums 7,6, and 5 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
The problems on this page are the property of the MAA's American Mathematics Competitions