Question

A complete cycle of a traffic light takes $60s$. During each cycle the light is green for $25s$, yellow for $5s$ and red for $30s$. At a randomly chosen time, the probability that the light will not be green is

• A. $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$3$}\right.$
• B. $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$4$}\right.$
• C. $\raisebox{1ex}{$7$}\!\left/ \!\raisebox{-1ex}{$12$}\right.$
• D. $\raisebox{1ex}{$3$}\!\left/ \!\raisebox{-1ex}{$4$}\right.$

Answer 1

The correct option is C

$\raisebox{1ex}{$7$}\!\left/ \!\raisebox{-1ex}{$12$}\right.$

Explanation for the correct answer:

Time for which light is not green in one cycle $=$ $Timeforwhichlightisred+Timeforwhichlightisyellow$

$$\begin{gathered} =30s+5s \\ =35s \end{gathered}$$

The probability that the light will not be green $=\frac{Timeforwhichlightisnotgreeninonecycle}{TotalTimeinonecycle}$

$$\begin{gathered} =\frac{35}{60} \\ =\frac{7}{12} \end{gathered}$$

Hence, correct option is (C).