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2002 AMC 12A Question 16

AMC12 · 2002 AMC 12A

Question 16

Tina randomly selects two distinct numbers from the set $\{1, 2, 3, 4, 5\},$ and Sergio randomly selects a number from the set $\{1, 2, \ldots, 10\}.$ The probability that Sergio’s number is larger than the sum of the two numbers chosen by Tina is
  1. $\dfrac{2}{5}$
  2. $\dfrac{9}{20}$
  3. $\dfrac{1}{2}$
  4. $\dfrac{11}{20}$
  5. $\dfrac{24}{25}$