Suppose that an employee at a local company checks his watch and realizes that he has 10 minutes to get to work on time. If he leaves now and does not get stopped by any traffic lights, he will arrive at work in exactly 8 minutes. In between his house and his work, there are three traffic lights, A, B, and C. Each light that stops him will cause him to arrive an additional 2 minutes later. The following table displays the probability that he is stopped by each of the three traffic lights. Assume that the probability that he is stopped by any given light is independent of the probability that he is stopped by any other light. What is the probability that the employee is not late for work?Traffic Light ATraffic Light BTraffic Light CP(A)P(B)P(C).3.4.6Please write your answer in decimal form, rounded to three decimal places.P(employee is not late for work) =

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Asked May 5, 2019
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Suppose that an employee at a local company checks his watch and realizes that he has 10 minutes to get to work on time. If he leaves now and does not get stopped by any traffic lights, he will arrive at work in exactly 8 minutes. In between his house and his work, there are three traffic lights, A, B, and C. Each light that stops him will cause him to arrive an additional 2 minutes later. The following table displays the probability that he is stopped by each of the three traffic lights. Assume that the probability that he is stopped by any given light is independent of the probability that he is stopped by any other light. What is the probability that the employee is not late for work?

Traffic Light A Traffic Light B Traffic Light C
P(A) P(B) P(C)
.3 .4 .6

Please write your answer in decimal form, rounded to three decimal places.

P(employee is not late for work) =

 

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Expert Answer

Step 1

Multiplication rule for independent events:

If two events A and B are independent then the multiplication rule state that:

 

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Step 2

Find the probability that employee is not late for work:

It is found that employee needs 10 minutes to get to work on time. If the person is not stopped by any traffic lights he will arrive at work in exactly 8 minutes. There are three traffic lights A, B, and C. Each light that stops him will cause him to arrive an additional 2...

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