SOLUTION: A parking lot has two entrances. Cars arrive at entrance 1 according to a Poisson distribution at an average of three per hour and at entrance 2 according to a Poisson distribution

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Question 328771: A parking lot has two entrances. Cars arrive at entrance 1 according to a Poisson distribution at an average of three per hour and at entrance 2 according to a Poisson distribution at an average of four per hour. What is the probability that a total of three cars at the parking lot in a given hour? (assume that the number of cars arriving at the two entrances are independent.)
Answer by jrfrunner(365) About Me  (Show Source):
You can put this solution on YOUR website!
X=cars arriving within an hour at entrance 1 P(X=x)=3%5Ex%2Ae%5E%28-3%29%2Fx%21
Y=cars arriving within an hour at entrance 2 P(Y=y)=4%5Ey%2Ae%5E%28-4%29%2Fy%21
Z=X+Y total cars arriving within one hour at both entrances P(Z=z)=7%5Ez%2Ae%5E%28-7%29%2Fz%21
P(Z=3)=7%5E3%2Ae%5E%28-7%29%2F3%21 = 0.052