### Brain Teasers

# Traffic Light

Probability
Probability puzzles require you to weigh all the possibilities and pick the most likely outcome.

There is a traffic light at the top of a hill. Cars can't see the light until they are 200 feet from the light.

The cycle of the traffic light is 30 seconds green, 5 seconds yellow and 20 seconds red.

A car is traveling 45 miles per hour up the hill.

What is the probability that the light will be yellow when the driver first crests the hill and that if the driver continues through the intersection at her present speed that she will run a red light?

The cycle of the traffic light is 30 seconds green, 5 seconds yellow and 20 seconds red.

A car is traveling 45 miles per hour up the hill.

What is the probability that the light will be yellow when the driver first crests the hill and that if the driver continues through the intersection at her present speed that she will run a red light?

### Answer

The probability of the driver encountering a yellow light and the light turning red before the car enters the intersection is about 5.5%.At 45 mph the car is traveling at 66 feet/second and will take just over 3 seconds (3.03) to travel the 200 feet to the intersection. Any yellow light that is in the last 3.03 seconds of the light will cause the driver to run a red light.

The entire cycle of the light is 55 seconds. 3.03/55 = 5.5%.

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