Cars cross a certain point in the highway in accordance with a Poisson process w

Question

Cars cross a certain point in the highway in accordance with a Poisson process
with rate =4 per minute.

(a) If Kate blindly runs across the highway, then what is the probability that she
will be uninjured if the amount of time that it takes her to cross the road is s seconds?
(Assume that if she is on the highway when a car passes by, then she will be injured.)
(b) Compute part (a) for s = 2; 5; 10; 20.
(c) Now assume that Kate is agile enough to escape from a single car, but if she
encounters two or more cars while attempting to cross the road, then she will be injured.
What is the probability that she will be unhurt if it takes her s seconds to cross?
(d) Compute part (c) for s = 5; 10; 20; 30.

Explanation / Answer

a) p(s;4)= (e^(-4))(4^s)/s! b) you substitute the formula and you should get: for s=2 you get: .1465 for s=5 you get : .1563 for s= 10 you get: .00053 for s=20 you get: 8.27 x 10^-9 c)2^s/s! d)for s=5 you get: .9834 for s=10 you get : .9999 for s=20 and 30 get : 1 hopefully i helped you, I answered as best as I can since your time was almos over, my battery was almost over, and you didnt have any other answer, if you have a graphic calculator you should be able to do them easily under stats section poisson, i hope you choose me as a good answer!

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