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

Options

A. `(1)/(3)`
B. `(1)/(4)`
C. `(4)/(12)`
D. `(7)/(12)`

Explanation

To solve the problem, we need to determine the probability that the traffic light is not green at a randomly chosen time.

### Step-by-step Solution:

1. **Understand the Cycle of the Traffic Light**:
- The complete cycle of the traffic light lasts for 60 seconds.
- During this cycle:
- Green light duration = 25 seconds
- Yellow light duration = 5 seconds
- Red light duration = 30 seconds

2. **Calculate the Total Time the Light is Not Green**:
- The light is not green during the yellow and red phases.
- Time not green = Yellow light duration + Red light duration
- Time not green = 5 seconds (yellow) + 30 seconds (red) = 35 seconds

3. **Calculate the Probability**:
- Probability (P) that the light is not green is given by the ratio of the time the light is not green to the total cycle time.
- P(not green) = (Time not green) / (Total cycle time)
- P(not green) = 35 seconds / 60 seconds

4. **Simplify the Probability**:
- P(not green) = 35/60
- P(not green) = 7/12 (after simplification)

### Final Answer:
The probability that the light will not be green at a randomly chosen time is **7/12**.