Exam P Practice Problem 44 – Traffic Statistics Using Poisson Distribution

Problem 44-A

The number of car accidents in a stretch of a highway (Highway #1) has a Poisson distribution with a mean of 4 per week. The number of car accidents in a stretch of another highway (Highway #2) has a Poisson distribution with a mean of 8 per week.

Assume that on a weekly basis, the number of accidents in one highway is independent of the number of accidents in the other highway.

In one particular week, exactly 5 auto accidents took place in these two highways. What is the probability that Highway #1 had exactly 2 accidents in this particular week?

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Problem 44-B

The number of cars (in a day) that break down in a stretch of a highway (Highway #1) has a Poisson distribution with a mean of 16. The number of cars (in a day) that break down in a stretch of another highway (Highway #2) has a Poisson distribution with a mean of 8.

Assume that on a daily basis, the number of cars breaking down in one highway is independent of the number of cars breaking down in the other highway.

In one particular day, exactly 8 cars were found to break down in these two highways. What is the probability that Highway #1 had exactly 5 cars breaking down in this particular day?

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Answers

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