Question

Imagine that a traffic intersection has a stop light that repeatedly cycles through the normal sequence of traffic signals (green light, yellow light, and red light). In each cycle the stop light is green for 25 s, yellow for 5 s, and red for 35 s. Assume that cars arrive at the intersection uniformly, which means that in any one interval of time, approximately the same number of cars arrive at the intersection at any other time interval of equal length.

Determine the probability that a car arrives at the intersection while the stop light is yellow. Give your answer as a percentage precise to two decimal places.

Answer 1

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Explanation:

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Answer 2

The probability in percentage of yellow is 7.69%.

How to calculate the probability of the yellow phase.

To determine the probability that a car arrives at the intersection while the stop light is yellow we need to consider the duration of the yellow light in relation to the total cycle time of the traffic signals

The total cycle time is the sum of the durations of each signal phase green( 25 seconds) , yellow( 5 seconds) and red( 35 seconds)

The total cycle time in seconds

= 25 + 5 + 35 = 65 seconds

The probability that a car arrives at the intersection while the stop light is yellow.

P(yellow) = total seconds yellow phase/total cycle time

P(Y) = 5/65

= 5/65 = 0.0769

In percentage

= 0.0769 * 100 = 7.69%

The probability in percentage of yellow is 7.69%