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Probability of odd products

Source: Problem #12 2016 AMC 10A

February 3, 2016
probabilityAMCAMC 10AMC 10 A2016 AMC 10A

Problem Statement

Three distinct integers are selected at random between 11 and 20162016, inclusive. Which of the following is a correct statement about the probability pp that the product of the three integers is odd?
<spanclass=′latex−bold′>(A)</span> p<18<spanclass=′latex−bold′>(B)</span> p=18<spanclass=′latex−bold′>(C)</span> 18<p<13<spanclass=′latex−bold′>(D)</span> p=13<spanclass=′latex−bold′>(E)</span> p>13<span class='latex-bold'>(A)</span>\ p<\dfrac{1}{8}\qquad<span class='latex-bold'>(B)</span>\ p=\dfrac{1}{8}\qquad<span class='latex-bold'>(C)</span>\ \dfrac{1}{8}<p<\dfrac{1}{3}\qquad<span class='latex-bold'>(D)</span>\ p=\dfrac{1}{3}\qquad<span class='latex-bold'>(E)</span>\ p>\dfrac{1}{3}
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