Question

The number of drilling rig accidents in a year can be modelled as a Poisson random
variable. Suppose that the expected number of serious accidents per year (for a certain
oil company) is λ =5. Find the probability that exactly 2 accidents will happen this year.

Answer 1

Let X be the random variable that denote number of accidents per year (for the oil company mentioned in the question)

X follows poisson distribution with $\small \lambda$ = 5 (mean)

Pmf of poisson distribution is :

$\small \frac{\lambda^{x}e^{-\lambda}}{x!}$

here we want the probability of exactly 2 accident occuring this year so, X = 2

52-5 P(X = 2) x²e 2! 0.0842 21

Answer: The probability that exactly 2 accidents will happen this year is 0.0842