Question

on average 3 traffic accidents per month occur at a certain intersection. what is the probability that in any given month at thisintersection exactly 5 accidents will occur?

Answer 1

Here we have to make an assumption that number of accidents at a certain intersection follows Poisson distribution. Let $X$ be the random

variable denoting the number of accidents in a month at a particular intersection:

$X\sim Po(\lambda)$

$$P(X=x)=\dfrac{e^{-\lambda}(\lambda)^x}{x!}$$

Given $\lambda=3$

The probability that in any given month at this intersection exactly 5 accidents will occur is

$$P(X=5)=\dfrac{e^{-3}(3)^5}{5!}=\dfrac{81}{40}e^{-3}\approx0.100819$$