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 A P(A) 0.4 Traffic light B P(B) 0.6 Traffic light C 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 three decimal places P(employee is not late for work)

Explanation / Answer

He any way takes 8 minutes to make to the office, he needs to there in 10 minutes.

So , he has 10 min - 8 min = 2 min to spare.

So, P(he' late)

= P(he' stopped at more than 1 traffic lights) [ since he' stopped by more than 1 traffic light, he' late by more than 2 minutes, since 1 traffic light takes 2 minutes to clear]

= 1- P( he' stopped by atmost 1)

= 1- ( P( he' stopped by 1 light only) - P( he' stopped by none )

= 1- ( .4*.4*.3 + .6*.3*.6+.6*.4*.7) - (.6*.4*.3)

= .604

[ please note that we can multiply probabilities here because they are independent

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