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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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 and solutions on this page are the property of the MAA's American Mathematics Competitions