{"status": "success", "data": {"description_md": "**POTD January 21, 2024**\n\nA coin is flipped $20$ times in a row. Given that exactly $14$ heads appeared, and the probability that no two consecutive coin flips were both tails can be written as $\\frac{m}{n}$, where $m, n$ are relatively prime positive integers, find the value of $m+n$.", "description_html": "<p><strong>POTD January 21, 2024</strong></p>&#10;<p>A coin is flipped <span class=\"katex--inline\">20</span> times in a row. Given that exactly <span class=\"katex--inline\">14</span> heads appeared, and the probability that no two consecutive coin flips were both tails can be written as <span class=\"katex--inline\">\\frac{m}{n}</span>, where <span class=\"katex--inline\">m, n</span> are relatively prime positive integers, find the value of <span class=\"katex--inline\">m+n</span>.</p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 3, "problem_name": "Problem of the Day #47", "can_next": false, "can_prev": false, "nxt": "", "prev": ""}}