Question

The number of traffic accidents per week in a small city has a Poisson distribution with mean 

equal to 1.3. What is the probability of at least two accidents in 2 weeks?

Answer 1

Let $X=$ the number of traffic accidents per week: $X\sim Po(\lambda t).$

Given $\lambda=1.3, t=2.$

$$P(X\ge 2)=1-P(X=0)-P(X=1)$$

$$=1-\dfrac{e^{-2.6}(2.6)^0}{0!}-\dfrac{e^{-2.6}(2.6)^1}{1!}\approx0.73261512$$