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Probability of Prime Numbers

Source: 2015 amc 10b #11

February 26, 2015
probabilitynumber theoryprime numbersAMC

Problem Statement

Among the positive integers less than 100100, each of whose digits is a prime number, one is selected at random. What is the probablility that the selected number is prime? <spanclass=′latex−bold′>(A)</span>899<spanclass=′latex−bold′>(B)</span>25<spanclass=′latex−bold′>(C)</span>920<spanclass=′latex−bold′>(D)</span>12<spanclass=′latex−bold′>(E)</span>916<span class='latex-bold'>(A) </span> \dfrac{8}{99} \qquad<span class='latex-bold'>(B) </span> \dfrac{2}{5} \qquad<span class='latex-bold'>(C) </span> \dfrac{9}{20} \qquad<span class='latex-bold'>(D) </span> \dfrac{1}{2} \qquad<span class='latex-bold'>(E) </span> \dfrac{9}{16}
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