{"status": "success", "data": {"description_md": "Three distinct integers are selected at random between $1$ and $2016$, inclusive. Which of the following is a correct statement about the probability $p$ that the product of the three integers is odd?\n\n$\\textbf{(A)}\\ p<\\dfrac{1}{8}\\qquad\\textbf{(B)}\\ p=\\dfrac{1}{8}\\qquad\\textbf{(C)}\\ \\dfrac{1}{8}<p<\\dfrac{1}{3}\\qquad\\textbf{(D)}\\ p=\\dfrac{1}{3}\\qquad\\textbf{(E)}\\ p>\\dfrac{1}{3}$", "description_html": "<p>Three distinct integers are selected at random between  <span class=\"katex--inline\">1</span>  and  <span class=\"katex--inline\">2016</span> , inclusive. Which of the following is a correct statement about the probability  <span class=\"katex--inline\">p</span>  that the product of the three integers is odd?</p>\n<p> <span class=\"katex--inline\">\\textbf{(A)}\\ p&lt;\\dfrac{1}{8}\\qquad\\textbf{(B)}\\ p=\\dfrac{1}{8}\\qquad\\textbf{(C)}\\ \\dfrac{1}{8}&lt;p&lt;\\dfrac{1}{3}\\qquad\\textbf{(D)}\\ p=\\dfrac{1}{3}\\qquad\\textbf{(E)}\\ p&gt;\\dfrac{1}{3}</span> </p>\n<hr><p>Full credit goes to <a href=\"https://maa.org/\">MAA</a> for authoring these problems. These problems were taken on the <a href=\"https://artofproblemsolving.com/\">AOPS</a> website.</p>", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 3, "problem_name": "2016 AMC 10A Problem 12", "can_next": true, "can_prev": true, "nxt": "/problem/16_amc10A_p13", "prev": "/problem/16_amc10A_p11"}}