Question

Suppose a certain traffic light shows a red light for 50 seconds, a green light for 50 seconds, and a yellow light for 5 seconds. If you look at this light at some randomly selected instant, what is the probability you will see a yellow or green light?

Answer 1

`P(Yellow\ or\ Green) = 0.524`

Explanation:

Given

`Yellow = 5\ seconds`

`Green = 50\ seconds`

`Red = 50\ seconds`

Required

Determine the probability of Green or Yellow

First, we need to determine the total time

`Total = 50 + 50 + 5`

`Total = 105\ seconds`

Next, is to determine the required probability

This is calculated as follows:

`P(Yellow\ or\ Green) = P(Yellow) + P(Green)`

`P(Yellow\ or\ Green) = (n(Yellow))/(Total) + (n(Green))/(Total)`

`P(Yellow\ or\ Green) = (5)/(105) + (50)/(105)`

`P(Yellow\ or\ Green) = (5 + 50)/(105)`

`P(Yellow\ or\ Green) = (55)/(105)`

`P(Yellow\ or\ Green) = 0.52380952381`

`P(Yellow\ or\ Green) = 0.524` -- Approximated