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**

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