Cars cross a road at a certain point according to a Poisson process with rate la

Question

Cars cross a road at a certain point according to a Poisson process with rate lamba = 6 per minute.

part a. If you run blindly across the road, then what is the probability that you will not be injured, if the amount of time it takes you to cross the road is 5 seconds? (Assume that if you are on the road when a car passes, then you will be injured.

part b. Now, you are agile enough to avoid a single car on the road, but if you encounter two or more cars when attempting to cross, then you will be injured. What is the probability that you cross uninjured if it still takes you 5 seconds to cross?

Explanation / Answer

X- no of cars crossing a road is Poisson with lamda =6

a) P(X=0 in 5 seconds)

Average for 5 seconds = 6/12 =0.5

Hence P(x=0 in 5 seconds) = 0.6065

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b) P(X<=1) = 0.9098

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