{"status": "success", "data": {"description_md": "When a certain biased coin is flipped five times, the probability of getting heads exactly once is not equal to $0$ and is the same as that of getting heads exactly twice. Let $\\frac ij$, in lowest terms, be the probability that the coin comes up heads in exactly $3$ out of $5$ flips. Find $i+j$.\n___\nLeading zeroes must be inputted, so if your answer is `34`, then input `034`. Full 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>When a certain biased coin is flipped five times, the probability of getting heads exactly once is not equal to <span class=\"katex--inline\">0</span> and is the same as that of getting heads exactly twice. Let <span class=\"katex--inline\">\\frac ij</span>, in lowest terms, be the probability that the coin comes up heads in exactly <span class=\"katex--inline\">3</span> out of <span class=\"katex--inline\">5</span> flips. Find <span class=\"katex--inline\">i+j</span>.</p>&#10;<hr><p>Leading zeroes must be inputted, so if your answer is <code>34</code>, then input <code>034</code>. 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": "1989 AIME Problem 5", "can_next": true, "can_prev": true, "nxt": "/problem/89_aime_p06", "prev": "/problem/89_aime_p04"}}