{"status": "success", "data": {"description_md": "At Rachelle's school an A counts 4 points, a B 3 points, a C 2 points, and a D 1 point. Her GPA on the four classes she is taking is computed as the total sum of points divided by 4. She is certain that she will get As in both Mathematics and Science, and at least a C in each of English and History. She thinks she has a $\\tfrac{1}{6}$ chance of getting an A in English, and a $\\tfrac{1}{4}$ chance of getting a B. In History, she has a $\\tfrac{1}{4}$ chance of getting an A, and a $\\tfrac{1}{3}$ chance of getting a B, independently of what she gets in English. What is the probability that Rachelle will get a GPA of at least 3.5?\n\n$\\textbf{(A)}\\; \\frac{11}{72} \\qquad\\textbf{(B)}\\; \\frac{1}{6} \\qquad\\textbf{(C)}\\; \\frac{3}{16} \\qquad\\textbf{(D)}\\; \\frac{11}{24} \\qquad\\textbf{(E)}\\; \\frac{1}{2}$\n___\nFull credit goes to [MAA](https://maa.org/) for authoring these problems. These problems were taken on the [AOPS](https://artofproblemsolving.com/) website.", "description_html": "<p>At Rachelle&#8217;s school an A counts 4 points, a B 3 points, a C 2 points, and a D 1 point. Her GPA on the four classes she is taking is computed as the total sum of points divided by 4. She is certain that she will get As in both Mathematics and Science, and at least a C in each of English and History. She thinks she has a  <span class=\"katex--inline\">\\tfrac{1}{6}</span>  chance of getting an A in English, and a  <span class=\"katex--inline\">\\tfrac{1}{4}</span>  chance of getting a B. In History, she has a  <span class=\"katex--inline\">\\tfrac{1}{4}</span>  chance of getting an A, and a  <span class=\"katex--inline\">\\tfrac{1}{3}</span>  chance of getting a B, independently of what she gets in English. What is the probability that Rachelle will get a GPA of at least 3.5?</p>&#10;<p> <span class=\"katex--inline\">\\textbf{(A)}\\; \\frac{11}{72} \\qquad\\textbf{(B)}\\; \\frac{1}{6} \\qquad\\textbf{(C)}\\; \\frac{3}{16} \\qquad\\textbf{(D)}\\; \\frac{11}{24} \\qquad\\textbf{(E)}\\; \\frac{1}{2}</span> </p>&#10;<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": "2015 AMC 12B Problem 15", "can_next": true, "can_prev": true, "nxt": "/problem/15_amc12B_p16", "prev": "/problem/15_amc12B_p14"}}