The number of traffic accidents that occur on a particular stretch of road during a month follows a Poisson distribution with a mean of 8.1. Find the probability that exactly three accidents will occur
On this stretch of road each of the next two months.
A)0.026886
B)0.000723
C)0.000065
D)0.053771

Question

Quizplus · Accepted Answer

The probability of exactly three accidents occurring in a given month is calculated using the Poisson distribution formula: $P(X=k) = \frac{\lambda^k e^{-\lambda}}{k!}$, where $\lambda$ is the mean number of occurrences (8.1 in this case), $k$ is the number of occurrences for which the probability is being calculated (3 accidents), and $e$ is the base of the natural logarithm. Plugging in the values, we get the probability for one month. Since we are looking for the probability of this happening in each of the next two months, and assuming each month is independent, we square the probability for one month to get the probability for two months.

The Number of Traffic Accidents That Occur on a Particular