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Tina and Sergio pick numbers

Source: AMC 2002 10A #24

February 11, 2008
probabilityAMC

Problem Statement

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\}. The probability that Sergio's number is larger than the sum of the two numbers chosen by Tina is <spanclass=latexbold>(A)</span> 2/5<spanclass=latexbold>(B)</span> 9/20<spanclass=latexbold>(C)</span> 1/2<spanclass=latexbold>(D)</span> 11/20<spanclass=latexbold>(E)</span> 24/25 <span class='latex-bold'>(A)</span>\ 2/5 \qquad <span class='latex-bold'>(B)</span>\ 9/20 \qquad <span class='latex-bold'>(C)</span>\ 1/2\qquad <span class='latex-bold'>(D)</span>\ 11/20 \qquad <span class='latex-bold'>(E)</span>\ 24/25