{"status": "success", "data": {"description_md": "For a particular peculiar pair of dice, the probabilities of rolling $1$, $2$, $3$, $4$, $5$, and $6$, on each die are in the ratio $1:2:3:4:5:6$. What is the probability of rolling a total of $7$ on the two dice? \n\n$\\mathrm{(A) \\ } \\frac{4}{63}\\qquad \\mathrm{(B) \\ } \\frac{1}{8}\\qquad \\mathrm{(C) \\ } \\frac{8}{63}\\qquad \\mathrm{(D) \\ } \\frac{1}{6}\\qquad \\mathrm{(E) \\ } \\frac{2}{7}$", "description_html": "<p>For a particular peculiar pair of dice, the probabilities of rolling  <span class=\"katex--inline\">1</span> ,  <span class=\"katex--inline\">2</span> ,  <span class=\"katex--inline\">3</span> ,  <span class=\"katex--inline\">4</span> ,  <span class=\"katex--inline\">5</span> , and  <span class=\"katex--inline\">6</span> , on each die are in the ratio  <span class=\"katex--inline\">1:2:3:4:5:6</span> . What is the probability of rolling a total of  <span class=\"katex--inline\">7</span>  on the two dice?</p>\n<p> <span class=\"katex--inline\">\\mathrm{(A) \\ } \\frac{4}{63}\\qquad \\mathrm{(B) \\ } \\frac{1}{8}\\qquad \\mathrm{(C) \\ } \\frac{8}{63}\\qquad \\mathrm{(D) \\ } \\frac{1}{6}\\qquad \\mathrm{(E) \\ } \\frac{2}{7}</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": 4, "problem_name": "2006 AMC 10B Problem 21", "can_next": true, "can_prev": true, "nxt": "/problem/06_amc10B_p22", "prev": "/problem/06_amc10B_p20"}}