Suppose that the cumulated number of cars on a freeway follows a Poisson process. We know that there are on average 10 cars per seconds at any point of the freeway. The freeway splits in two branches, and drivers decide indepen- dently to go on the left branch or on the right branch with probability 50%. What is the probability that the total number of cars entering the left branch over 10 seconds is less than or equal to 5?

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 31E
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Suppose that the cumulated number of cars on a freeway follows a Poisson
process. We know that there are on average 10 cars per seconds at any point
of the freeway. The freeway splits in two branches, and drivers decide indepen-
dently to go on the left branch or on the right branch with probability 50%.
What is the probability that the total number of cars entering the left branch
over 10 seconds is less than or equal to 5?
Transcribed Image Text:Suppose that the cumulated number of cars on a freeway follows a Poisson process. We know that there are on average 10 cars per seconds at any point of the freeway. The freeway splits in two branches, and drivers decide indepen- dently to go on the left branch or on the right branch with probability 50%. What is the probability that the total number of cars entering the left branch over 10 seconds is less than or equal to 5?
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