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

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?

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Edana Edana 5 years 2021-08-03T14:35:15+00:00 1 Answers 17 views 0

Answers ( )

  1. King
    0
    2021-08-03T14:37:10+00:00
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    Answer:

    y = 12

    Step-by-step 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

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