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2002 AMC 10AProblem 24P21-25~5 minPrint
Basic ProbabilityBasic CountingOrganized listing / direct enumerationSplit into exhaustive cases and handle each

Tina randomly selects two distinct numbers from the set {1,2,3,4,5}\{ 1, 2, 3, 4, 5 \} , and Sergio randomly selects a number from the set {1,2,...,10}\{ 1, 2, ..., 10 \} . What is the probability that Sergio's number is larger than the sum of the two numbers chosen by Tina?

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Problem © Mathematical Association of America (MAA), American Mathematics Competitions. Reproduced for non-commercial educational use. Solution and commentary are original to this site. Also appeared as 2002 12A #16.