Question

On average, 3 accidents happen every week along Great North Road. What is the probability that we will observe 9 accidents in a month? 

Answer 1

Let $x=$ the number of accidents happened: $x\sim Po(\lambda t)$

Given $\lambda=3, t=4$

$$P(x=9)=\dfrac{e^{-3(4)}\cdot(3(4) )^9}{9!}=0.087364$$

The probability that we will observe 9 accidents in a month is 0.087364.