UPSC Prelims 2002 Q1: Science & Technology – Quantitative Aptitude
A complete cycle of a traffic light takes 60 seconds. During each cycle the light is green for 25
seconds, yellow for 5 seconds and red for 30 seconds. At a randomly chosen time, the probability
that the light will not be green is
- (a) 1/3
- (b) 1/4
- (c) 5/12
- (d) 7/12
Answer: (d) 7/12
Explanation
Probability that the traffic light is not green
| Colour | Seconds in a 60-second cycle |
|---|---|
| Green | 25 seconds |
| Yellow | 5 seconds |
| Red | 30 seconds |
| Not green (yellow + red) | 5 + 30 = 35 seconds |
The light is not green for 35 seconds out of every 60. At a randomly chosen time, the probability that the light will not be green is 35/60 = 7/12. The same answer comes from 1 − 25/60 = 35/60.
Answer: (d) 7/12.
Why each option is right or wrong
- (a) Incorrect. 1/3 is 20 seconds out of 60, which matches no colour.
- (b) Incorrect. 1/4 is 15 seconds out of 60.
- (c) Incorrect. 5/12 is 25/60, the probability that the light IS green.
- (d) CORRECT. 35/60 = 7/12 is the chance of not green.
Key point
Probability = favourable time ÷ total cycle time; the complement rule gives P(not green) = 1 − P(green).
Remember
P(not green) = (5 + 30)/60 = 7/12.
Common mistakes
- Choosing 5/12, which is the probability of green, not of not-green.
- Counting only red (30/60 = 1/2) and forgetting yellow.
- Leaving the fraction unreduced and then mismatching it with an option.
Exam tip
Read the word NOT first, then use 1 − P(event) as a quick cross-check.
Sources
- NCERT Class X Mathematics — Probability
- NCERT Class XI Mathematics — Probability