Suppose a certain traffic light shows a red light for 42 seconds, a green light for 45 seconds, and a yellow light for 5 seconds. each day you look at this light at a randomly chosen instant. what is the probability you see a red light five days in a row?

Red light time = 42 seconds

Green light time = 45 seconds

Yellow light time = 5 seconds

Total Time of all lights i (Red Light time + Green light time + Yellow light time)

= 42 + 45 + 5 = 92 seconds

Probability to see Red light in a day

P (Red) = (Red light time) / (Total time of all lights)

Probability to see Red light 5 days in a row

P (Red) = (Red light time) ^5 / (Total time of all lights) ^5

P (Red) = (42) ⁵ / (92) ⁵

P (Red) = 0.01689

Probability to see Red light 5 days in a row = 1.689%

The time of a red light = 42 seconds

The time of a green light = 45 seconds

The time of a yellow light = 5 seconds

so,

All times = 42 + 45 + 5 = 92 seconds

Then

The probability to see a red light in one day = P (red) = (The time of a red light) : (all tmes)

So, P (red) = 42/95

And

The probability to see a red light in five days = {P (red) }⁵ = (42/95) ⁵

= 0.01689

= 1.689 %