{"status": "success", "data": {"description_md": "There are lily pads in a row numbered $0$ to $11$, in that order. There are predators on lily pads $3$ and $6$, and a morsel of food on lily pad $10$. Fiona the frog starts on pad $0$, and from any given lily pad, has a $\\frac{1}{2}$ chance to hop to the next pad, and an equal chance to jump $2$ pads. What is the probability that Fiona reaches pad $10$ without landing on either pad $3$ or pad $6$?\n\n$\\textbf{(A) } \\frac{15}{256} \\qquad \\textbf{(B) } \\frac{1}{16} \\qquad \\textbf{(C) } \\frac{15}{128}\\qquad \\textbf{(D) } \\frac{1}{8} \\qquad \\textbf{(E) } \\frac14$\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>There are lily pads in a row numbered  <span class=\"katex--inline\">0</span>  to  <span class=\"katex--inline\">11</span> , in that order. There are predators on lily pads  <span class=\"katex--inline\">3</span>  and  <span class=\"katex--inline\">6</span> , and a morsel of food on lily pad  <span class=\"katex--inline\">10</span> . Fiona the frog starts on pad  <span class=\"katex--inline\">0</span> , and from any given lily pad, has a  <span class=\"katex--inline\">\\frac{1}{2}</span>  chance to hop to the next pad, and an equal chance to jump  <span class=\"katex--inline\">2</span>  pads. What is the probability that Fiona reaches pad  <span class=\"katex--inline\">10</span>  without landing on either pad  <span class=\"katex--inline\">3</span>  or pad  <span class=\"katex--inline\">6</span> ?</p>&#10;<p> <span class=\"katex--inline\">\\textbf{(A) } \\frac{15}{256} \\qquad \\textbf{(B) } \\frac{1}{16} \\qquad \\textbf{(C) } \\frac{15}{128}\\qquad \\textbf{(D) } \\frac{1}{8} \\qquad \\textbf{(E) } \\frac14</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": "2019 AMC 12B Problem 16", "can_next": true, "can_prev": true, "nxt": "/problem/19_amc12B_p17", "prev": "/problem/19_amc12B_p15"}}