Question

During a 2-week period, the average number of accidents on this section of highway is 4. What is the probability of at most two accidents during a 2-week period?

Answer 1

Let $X=$ the number of  accidents on this section of highway during a

2-week period: $X \sim Po(\lambda)$

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

Given $\lambda=4$

$$P(X\leq2)=P(X=0)+P(X=1)+P(X=2)$$

$$=\dfrac{e^{-4}\cdot4^0}{0!}+\dfrac{e^{-4}\cdot4^1}{1!}+\dfrac{e^{-4}\cdot4^2}{2!}$$

$$=13e^{-4}\approx0.238103$$

The probability of at most two accidents during a 2-week period is 0.238103.