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Find the probability that at least one of each of car types

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Cars pass an intersection according to a Poisson process with rate λ. There are 4 types of cars, and each passing car is, independently, type i with probability pi, 4 i=1 pi = 1.

(a) Find the probability that at least one of each of car types 1, 2, 3 but none of type 4 have passed by time t .

(b) Given that exactly 6 cars of type 1 or 2 passed by time t,  find the probability that 4 of them were type 1

Reference no: EM132852884

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