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?
Answer Choices
A. \frac12
B. \frac14
C. \frac25
D. \frac{3}{10}
E. \frac{7}{20}