Question

The average number of traffic accidents on a certain section of highway is two per week. Assume that the number of accidents follow a Poisson distribution with μ = 2. Find the probability of at least 2 accidents on this section of highway during a week period.

Answer 1

Answer on Question #71063 – Math – Statistics and Probability

Question

The average number of traffic accidents on a certain section of highway is two per week. Assume that the number of accidents follow a Poisson distribution with $\mu = 2$. Find the probability of at least 2 accidents on this section of highway during a week period.

Solution

Let $X$ be a random variable denoting the number of accidents on a particular section of highway during a week.

We know, $X \sim \text{Poisson}(2)$

$$P(X = a) = \left(\frac{e^{-2} 2^{a}}{a!}\right) \quad \text{Equation (1)}$$

We need to find

$$\begin{aligned} P(X &\geq 2) = 1 - P(X &= 0) - P(X &= 1) \\ &= 1 - \frac{e^{-2}}{2} - \frac{e^{-2}}{2} \quad \text{.[Putting } a=0 \text{ and } a=1 \text{ in Equation (1)}] \\ &= 1 - 3e^{-2} \end{aligned}$$

Answer: $1 - 3e^{-2}$

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