MathDB
Red Ball is Superior

Source: 2019 AMC 12B #13 / AMC 10B #17

February 14, 2019
2019 AMC 12BAMCAMC 12AMC 12 Bprobability2019 AMC2019 AMC 10B

Problem Statement

A red ball and a green ball are randomly and independently tossed into bins numbered with positive integers so that for each ball, the probability that it is tossed into bin kk is 2−k2^{-k} for k=1,2,3,….k=1,2,3,\ldots. What is the probability that the red ball is tossed into a higher-numbered bin than the green ball?
<spanclass=′latex−bold′>(A)</span>14<spanclass=′latex−bold′>(B)</span>27<spanclass=′latex−bold′>(C)</span>13<spanclass=′latex−bold′>(D)</span>38<spanclass=′latex−bold′>(E)</span>37<span class='latex-bold'>(A) </span> \frac{1}{4} \qquad<span class='latex-bold'>(B) </span> \frac{2}{7} \qquad<span class='latex-bold'>(C) </span> \frac{1}{3} \qquad<span class='latex-bold'>(D) </span> \frac{3}{8} \qquad<span class='latex-bold'>(E) </span> \frac{3}{7}
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