Suppose that an employee at a local company checks his watch and realizes that h

Question

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. Traffic light ATraffic light BTraffic light C P(B) 0.6 P(A) 0.4 P(C) 0.7 What is the probability that the employee is not late for work? Please write your answer in decimal form, rounded to threie decimal places Pemployee is not late for work) = .072

Explanation / Answer

Ans:

As,he will reach in 8 min,if no light stops him and 10 min if one light stops him,so he can reach in time if atmost one of the light stops him.

P(either only one light stops him or none of the stops him)

=P(none)+P(one of light stops)

=(1-0.4)*(1-0.6)*(1-0.7)+0.4*(1-0.6)*(1-0.7)+(1-0.4)*0.6*(1-0.7)+(1-0.4)*(1-0.6)*0.7

=0.6*0.4*0.3+0.4*0.4*0.3+0.6*0.6*0.3+0.6*0.4*0.7

=0.072+0.048+0.108+0.168

=0.396

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