Question

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?

Answer 1

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%

Answer 2

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 %