Question

Assume that the Poisson distribution applies and that the mean number of aircraft accidents is 10 per month. Find P(0), the probability that in a month, there will be no aircraft accidents. Is it unlikely to have a month with no aircraft accidents?

Answer 1

Poisson random variable has probability mass function :

where,

We need to find :

Probability that in a month, there will be no aircraft accidents = P(0) = P(X=0)

We have :

So,

So,

Probability that in a month, there will be no aircraft accidents = 0.00005

Yes, it is unlikely to have a month with no aircraft as the probability that there will be no aircraft accidents is very small and close to zero.