{"status": "success", "data": {"description_md": "Each face of a cube is painted either red or blue, each with probability $\\frac12$. The color of each face is determined independently. What is the probability that the painted cube can be placed on a horizontal surface so that the four vertical faces are all the same color?\n\n$\\textbf{(A)}\\ \\frac14 \\qquad \\textbf{(B)}\\ \\frac {5}{16} \\qquad \\textbf{(C)}\\ \\frac38 \\qquad \\textbf{(D)}\\ \\frac {7}{16} \\qquad \\textbf{(E)}\\ \\frac12$\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>Each face of a cube is painted either red or blue, each with probability <span class=\"katex--inline\">\\frac12</span>. The color of each face is determined independently. What is the probability that the painted cube can be placed on a horizontal surface so that the four vertical faces are all the same color?</p>&#10;<p><span class=\"katex--inline\">\\textbf{(A)}\\ \\frac14 \\qquad \\textbf{(B)}\\ \\frac {5}{16} \\qquad \\textbf{(C)}\\ \\frac38 \\qquad \\textbf{(D)}\\ \\frac {7}{16} \\qquad \\textbf{(E)}\\ \\frac12</span></p>&#10;<hr/>&#10;<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>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 3, "problem_name": "2004 AMC 12B Problem 20", "can_next": true, "can_prev": true, "nxt": "/problem/04_amc12B_p21", "prev": "/problem/04_amc12B_p19"}}