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Divisibility Probability

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January 2, 2009
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Problem Statement

What is the probability that an integer in the set {1,2,3,…,100} \{1,2,3,\ldots,100\} is divisible by 2 2 and not divisible by 3 3? <spanclass=′latex−bold′>(A)</span> 16<spanclass=′latex−bold′>(B)</span> 33100<spanclass=′latex−bold′>(C)</span> 1750<spanclass=′latex−bold′>(D)</span> 12<spanclass=′latex−bold′>(E)</span> 1825 <span class='latex-bold'>(A)</span>\ \frac{1}{6} \qquad <span class='latex-bold'>(B)</span>\ \frac{33}{100} \qquad <span class='latex-bold'>(C)</span>\ \frac{17}{50} \qquad <span class='latex-bold'>(D)</span>\ \frac{1}{2} \qquad <span class='latex-bold'>(E)</span>\ \frac{18}{25}
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