Exercice on the sum of independent Poisson random variables

erikhadife

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I am struggling to solve this problem, please help!

Cars pass a point on a busy road at an average rate of 150 per hour. Assume that the number of cars in an hour follows a Poisson distribution. Other motor vehicles (lorries, motorcycles etc.) pass the same point at the rate of 75 per hour. Assume a Poisson distribution for these vehicles too, and assume that the number of other vehicles is independent of the number of cars.
(a) What is the probability that one car and one other motor vehicle pass in a two minute period?
b) What is the probability that two motor vehicles of any type (cars, lorries,
motorcycles etc.) pass in a two-minute period
 
I am struggling to solve this problem, please help!

Cars pass a point on a busy road at an average rate of 150 per hour. Assume that the number of cars in an hour follows a Poisson distribution. Other motor vehicles (lorries, motorcycles etc.) pass the same point at the rate of 75 per hour. Assume a Poisson distribution for these vehicles too, and assume that the number of other vehicles is independent of the number of cars.
(a) What is the probability that one car and one other motor vehicle pass in a two minute period?
If A and B are independent events then P(A and B)= P(A)P(B).
What is the probability that one car will pass in two minutes? What is the probability that one other motor vehicle will pass in two minutes?

(b) What is the probability that two motor vehicles of any type (cars, lorries,
motorcycles etc.) pass in a two-minute period
If A and B are mutually exclusive events then P(A or B)= P(A)+ P(B). Here, the two motor vehicles can be "two cars" or "one car and one other vehicle" or "two other vehicles".
 
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