{"status": "success", "data": {"description_md": "Objects $A$ and $B$ move simultaneously in the coordinate plane via a sequence of steps, each of length one. Object $A$ starts at $(0,0)$ and each of its steps is either right or up, both equally likely. Object $B$ starts at $(5,7)$ and each of its steps is either to the left or down, both equally likely. Which of the following is closest to the probability that the objects meet?\n\n$\\mathrm{(A)} \\ 0.10 \\qquad<br>\\mathrm{(B)} \\ 0.15 \\qquad<br>\\mathrm{(C)} \\ 0.20 \\qquad<br>\\mathrm{(D)} \\ 0.25 \\qquad<br>\\mathrm{(E)} \\ 0.30 \\qquad$\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>Objects  <span class=\"katex--inline\">A</span>  and  <span class=\"katex--inline\">B</span>  move simultaneously in the coordinate plane via a sequence of steps, each of length one. Object  <span class=\"katex--inline\">A</span>  starts at  <span class=\"katex--inline\">(0,0)</span>  and each of its steps is either right or up, both equally likely. Object  <span class=\"katex--inline\">B</span>  starts at  <span class=\"katex--inline\">(5,7)</span>  and each of its steps is either to the left or down, both equally likely. Which of the following is closest to the probability that the objects meet?</p>&#10;<p> <span class=\"katex--inline\">\\mathrm{(A)} \\ 0.10 \\qquad\\mathrm{(B)} \\ 0.15 \\qquad\\mathrm{(C)} \\ 0.20 \\qquad\\mathrm{(D)} \\ 0.25 \\qquad\\mathrm{(E)} \\ 0.30 \\qquad</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": 5, "problem_name": "2003 AMC 12A Problem 22", "can_next": true, "can_prev": true, "nxt": "/problem/03_amc12A_p23", "prev": "/problem/03_amc12A_p21"}}