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

Answer:

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

Step-by-step 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:

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

$P(Yellow\ or\ Green) = \frac{n(Yellow)}{Total} + \frac{n(Green)}{Total}$

$P(Yellow\ or\ Green) = \frac{5}{105} + \frac{50}{105}$

$P(Yellow\ or\ Green) = \frac{5 + 50}{105}$

$P(Yellow\ or\ Green) = \frac{55}{105}$

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

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