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

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Q: 1 (IAS/2002)
A complete cycle of a traffic light takes 60 seconds. During each cycle the light is green for 25 second, yellow for 5 second and red for 30 second. At a randomly chosen time, the probability that the light will not be green is

question_subject: 

Maths

question_exam: 

IAS

stats: 

0,6,11,3,1,7,6

keywords: 

{'traffic light': [0, 0, 1, 0], 'probability': [0, 3, 3, 0], 'complete cycle': [0, 0, 1, 0], 'cycle': [0, 2, 5, 2], 'seconds': [3, 3, 8, 6], 'light': [16, 4, 34, 62]}

To find the probability that the light will not be green at a randomly chosen time, we need to consider the time when the light is yellow or red.

The total time for one complete cycle of the traffic light is 60 seconds.

The light is green for 25 seconds, yellow for 5 seconds, and red for 30 seconds.

Therefore, the probability that the light will not be green is the sum of the probabilities of it being yellow or red.

Probability of the light being yellow = time for yellow / total time = 5 / 60 = 1 / 12

Probability of the light being red = time for red / total time = 30 / 60 = 1 / 2

Probability that the light will not be green = Probability of being yellow + Probability of being red

= 1/12 + 1/2

= 7/12

Therefore, the probability that the light will not be green at a randomly chosen time is 7/12.