A parking lot has two entrances. Cars arrive at entrance I according to a Poisson distribution at an average of 3 per hour and at entrance II according to a Poisson distribution at an average of 2 per hour. What is the probability that a total of 3 cars will arrive at the parking lot in a given hour? What is the probability that less than 3 cars will arrive at the parking lot in a given hour?

Question

Mathematics

Cooper Knox

6 March, 03:57

A parking lot has two entrances. Cars arrive at entrance I according to a Poisson distribution at an average of 3 per hour and at entrance II according to a Poisson distribution at an average of 2 per hour. What is the probability that a total of 3 cars will arrive at the parking lot in a given hour? What is the probability that less than 3 cars will arrive at the parking lot in a given hour?

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Answers (1)

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Patrick Townsend · Answer 1

P (X=3cars) = 0.052

P (X>3 cars) = 0.00638

Step-by-step explanation:

In total there are 7 cars per hour.

Using formulae for geometric Probability

P (X=3) = (7^3*e-7) / 3! = 0.0521

P (X>3cars) = (7^2 * e-7) / 2! =

P (X>3) = 0.0128/2*1 = 0.00638