{"status": "success", "data": {"description_md": "Jerry starts at $0$ on the real number line. He tosses a fair coin $8$ times. When he gets heads, he moves $1$ unit in the positive direction; when he gets tails, he moves $1$ unit in the negative direction. The probability that he reaches $4$ at some time during this process is $\\frac{a}{b},$ where $a$ and $b$ are relatively prime positive integers. What is $a + b?$ (For example, he succeeds if his sequence of tosses is $HTHHHHHH.$)\n\n$\\textbf{(A)}\\ 69\\qquad\\textbf{(B)}\\ 151\\qquad\\textbf{(C)}\\ 257\\qquad\\textbf{(D)}\\ 293\\qquad\\textbf{(E)}\\ 313$\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>Jerry starts at  <span class=\"katex--inline\">0</span>  on the real number line. He tosses a fair coin  <span class=\"katex--inline\">8</span>  times. When he gets heads, he moves  <span class=\"katex--inline\">1</span>  unit in the positive direction; when he gets tails, he moves  <span class=\"katex--inline\">1</span>  unit in the negative direction. The probability that he reaches  <span class=\"katex--inline\">4</span>  at some time during this process is  <span class=\"katex--inline\">\\frac{a}{b},</span>  where  <span class=\"katex--inline\">a</span>  and  <span class=\"katex--inline\">b</span>  are relatively prime positive integers. What is  <span class=\"katex--inline\">a + b?</span>  (For example, he succeeds if his sequence of tosses is  <span class=\"katex--inline\">HTHHHHHH.</span> )</p>&#10;<p> <span class=\"katex--inline\">\\textbf{(A)}\\ 69\\qquad\\textbf{(B)}\\ 151\\qquad\\textbf{(C)}\\ 257\\qquad\\textbf{(D)}\\ 293\\qquad\\textbf{(E)}\\ 313</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": "2016 AMC 12A Problem 19", "can_next": true, "can_prev": true, "nxt": "/problem/16_amc12A_p20", "prev": "/problem/16_amc12A_p18"}}