Question

The number of traffic accidents at a certain intersection is thought to be well modeled by a Poisson process with a mean of 3.5 accidents per year

If no accidents have occurred within the last six months, what is the probability that an accident will occur within the next year?

Answer 1

Answer:-

let the number of accidents that occur in a year be X.Then we are given that

X~Poisson(3.5)

Poisson distribution follows a memoryless property therefore the probability that there will be an accident next year given there was no accident in last 6 months is equal to the probability of an accident in the next year without any condition.

Let be the number of accident in next year .Then we get:

Y~Poisson(3.5)

Therefore we simply have to find:

Therefore poisson distribution probability formula we get:

Therefore 0.9699 is the required probability