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Source: 2017 AMC10B #9

February 16, 2017
AMCAMC 10AMC 10 Bprobability2017 AMC 10B

Problem Statement

A radio program has a quiz consisting of 33 multiple-choice questions, each with 33 choices. A contestant wins if he or she gets 22 or more of the questions right. The contestant answers randomly to each question. What is the probability of winning?
<spanclass=′latex−bold′>(A)</span>127<spanclass=′latex−bold′>(B)</span>19<spanclass=′latex−bold′>(C)</span>29<spanclass=′latex−bold′>(D)</span>727<spanclass=′latex−bold′>(E)</span>12<span class='latex-bold'>(A) </span> \frac{1}{27}\qquad <span class='latex-bold'>(B) </span> \frac{1}{9}\qquad <span class='latex-bold'>(C) </span> \frac{2}{9}\qquad <span class='latex-bold'>(D) </span> \frac{7}{27}\qquad <span class='latex-bold'>(E) </span> \frac{1}{2}
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