{"status": "success", "data": {"description_md": "Nylah has her living room lights on a timer. Each evening, the timer switches the lights on randomly at exactly 7:00 p.m., 7:30 p.m., 8:00 p.m., 8:30 p.m., or 9:00 p.m. Later in the evening, the timer switches the lights off at any random time between 11 p.m. and 1 a.m. For example, the lights could be switched on at exactly 7:30 p.m. and off at any one of the infinite number of possible times between 11 p.m. and 1 a.m. On a given night, Nylah's lights are on for $t$ hours. What is the probability that $4 < t < 5$?\n\n$\\text{(A)}\\ \\frac{1}{2}\\qquad\\text{(B)}\\ \\frac{1}{4}\\qquad\\text{(C)}\\ \\frac{2}{5}\\qquad\\text{(D)}\\ \\frac{3}{10}\\qquad\\text{(E)}\\ \\frac{7}{20}$\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>Nylah has her living room lights on a timer. Each evening, the timer switches the lights on randomly at exactly 7:00 p.m., 7:30 p.m., 8:00 p.m., 8:30 p.m., or 9:00 p.m. Later in the evening, the timer switches the lights off at any random time between 11 p.m. and 1 a.m. For example, the lights could be switched on at exactly 7:30 p.m. and off at any one of the infinite number of possible times between 11 p.m. and 1 a.m. On a given night, Nylah's lights are on for <span class=\"katex--inline\">t</span> hours. What is the probability that <span class=\"katex--inline\">4 &lt; t &lt; 5</span>?</p>\n<p><span class=\"katex--inline\">\\text{(A)}\\ \\frac{1}{2}\\qquad\\text{(B)}\\ \\frac{1}{4}\\qquad\\text{(C)}\\ \\frac{2}{5}\\qquad\\text{(D)}\\ \\frac{3}{10}\\qquad\\text{(E)}\\ \\frac{7}{20}</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": "2015 Cayley Problem 23", "can_next": true, "can_prev": true, "nxt": "/problem/15_cayley_p24", "prev": "/problem/15_cayley_p22"}}