{"status": "success", "data": {"description_md": "Amina and Bert alternate turns tossing a fair coin. Amina goes first and each player takes three turns. The first player to toss a tail wins. If neither Amina nor Bert tosses a tail, then neither wins. What is the probability that Amina wins?\n\n$\\text{(A)}\\ \\frac{21}{32}\\qquad\\text{(B)}\\ \\frac{5}{8}\\qquad\\text{(C)}\\ \\frac{3}{7}\\qquad\\text{(D)}\\ \\frac{11}{16}\\qquad\\text{(E)}\\ \\frac{9}{16}$\n\n___\n\n**[Fermat](https://www.cemc.uwaterloo.ca/contests/past_contests.html#pcf), by [CEMC](https://cemc.uwaterloo.ca/), is licensed under the [CC BY-NC 3.0 DEED](https://creativecommons.org/licenses/by-nc/3.0/). They are not affiliated with or endorse TopsOJ in any way.**\n", "description_html": "<p>Amina and Bert alternate turns tossing a fair coin. Amina goes first and each player takes three turns. The first player to toss a tail wins. If neither Amina nor Bert tosses a tail, then neither wins. What is the probability that Amina wins?</p>\n<p><span class=\"katex--inline\">\\text{(A)}\\ \\frac{21}{32}\\qquad\\text{(B)}\\ \\frac{5}{8}\\qquad\\text{(C)}\\ \\frac{3}{7}\\qquad\\text{(D)}\\ \\frac{11}{16}\\qquad\\text{(E)}\\ \\frac{9}{16}</span></p>\n<hr>\n<p><strong><a href=\"https://www.cemc.uwaterloo.ca/contests/past_contests.html#pcf\">Fermat</a>, by <a href=\"https://cemc.uwaterloo.ca/\">CEMC</a>, is licensed under the <a href=\"https://creativecommons.org/licenses/by-nc/3.0/\">CC BY-NC 3.0 DEED</a>. They are not affiliated with or endorse TopsOJ in any way.</strong></p>\n", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 3, "problem_name": "2015 Fermat Problem 21", "can_next": true, "can_prev": true, "nxt": "/problem/15_fermat_p22", "prev": "/problem/15_fermat_p20"}}