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Sum of dice is 7

Source: 2022 AMC 10B P12

November 17, 2022
probabilityAMCAMC 102022 AMC2022 AMC 10BDice

Problem Statement

A pair of fair 66-sided dice is rolled nn times. What is the least value of nn such that the probability that the sum of the numbers face up on a roll equals 77 at least once is greater than 12\frac{1}{2}?
<spanclass=latexbold>(A)</span>2<spanclass=latexbold>(B)</span>3<spanclass=latexbold>(C)</span>4<spanclass=latexbold>(D)</span>5<spanclass=latexbold>(E)</span>6<span class='latex-bold'>(A) </span> 2 \qquad <span class='latex-bold'>(B) </span> 3 \qquad <span class='latex-bold'>(C) </span> 4 \qquad <span class='latex-bold'>(D) </span> 5 \qquad <span class='latex-bold'>(E) </span> 6