{"status": "success", "data": {"description_md": "One bag contains 2 red marbles and 2 blue marbles. A second bag contains 2 red marbles, 2 blue marbles, and $g$ green marbles, with $g > 0$. For each bag, Maria calculates the probability of randomly drawing two marbles of the same colour in two draws from that bag, without replacement. (Drawing two marbles *without replacement* means drawing two marbles, one after the other, without putting the first marble back into the bag.) If these two probabilities are equal, then the value of $g$ is\n\n$\\text{(A)}\\ 4\\qquad\\text{(B)}\\ 5\\qquad\\text{(C)}\\ 6\\qquad\\text{(D)}\\ 7\\qquad\\text{(E)}\\ 8$\n\n___\n\n**[Cayley](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>One bag contains 2 red marbles and 2 blue marbles. A second bag contains 2 red marbles, 2 blue marbles, and <span class=\"katex--inline\">g</span> green marbles, with <span class=\"katex--inline\">g &gt; 0</span>. For each bag, Maria calculates the probability of randomly drawing two marbles of the same colour in two draws from that bag, without replacement. (Drawing two marbles *without replacement* means drawing two marbles, one after the other, without putting the first marble back into the bag.) If these two probabilities are equal, then the value of <span class=\"katex--inline\">g</span> is</p>\n<p><span class=\"katex--inline\">\\text{(A)}\\ 4\\qquad\\text{(B)}\\ 5\\qquad\\text{(C)}\\ 6\\qquad\\text{(D)}\\ 7\\qquad\\text{(E)}\\ 8</span></p>\n<hr>\n<p><strong><a href=\"https://www.cemc.uwaterloo.ca/contests/past_contests.html#pcf\">Cayley</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": "2013 Cayley Problem 23", "can_next": true, "can_prev": true, "nxt": "/problem/13_cayley_p24", "prev": "/problem/13_cayley_p22"}}