Question

Michael goes through the same traffic light each day on his way home from work. This year, the traffic light has been green 28 times, red 35 times, and yellow y times when he drives upto it. Michael uses the probability of traffic light being yellow to predict that 16 of the next 100 times he reaches the traffic light, it will be yellow. What is the value of y?

Answer 1

y = 12

Explanation:

Given

Green = 28

Red = 35

Yellow = y

Prediction of yellow = 16 of 100

Required

Determine y

First, we need to calculate the probability of yellow.

Probability of yellow =

Probability = Yellow/Total

Where

Total = Yellow + Red + Green

Total = y + 35 + 28

Total = y + 63

So,

Probability = y/(y + 63)

Also, the prediction of yellow is 16 out of 100.

Represent this as probability.

Probability = 16/100

Equate both expressions to solve for y

y/(y + 63) = 16/100

y/(y + 63) = 0.16

Multiply both sides by (y + 63)

y = 0.16(y + 63(

y = 0.16y + 10.08

Collect like terms

y - 0.16y = 10.08

0.84y = 10.08

Solve for y

y = 10.08/0.84

y = 12