The number of traffic accidents that occur on a particular stretch of road during a month follows a Poissondistribution with a mean of 6.3. Find the probability that the next two months will both result in five accidentseach occurring on this stretch of road.
A) 0.023064
B) 0.151868
C) 0.303736
D) 0.008924

Question

Quizplus · Accepted Answer

The probability of observing exactly $k$ events in a Poisson distribution is given by $P(X=k) = \frac{e^{-\lambda} \lambda^k}{k!}$, where $\lambda$ is the mean number of events. For two independent months with 5 accidents each, the probability is $P(X=5)^2$. Given $\lambda = 6.3$, $P(X=5) = \frac{e^{-6.3} 6.3^5}{5!}$. Calculating this gives $P(X=5) \approx 0.151868$, and squaring this probability gives approximately $0.023064$, which matches option A.

The Number of Traffic Accidents That Occur on a Particular