Question

In a certain geographic area a heavy rainfall occurs on the average two times per three months. Find the probability that during the next two months there will be more than four heavy rainfalls in this area.

Answer 1

This is a Poisson Distribution
Average over 3 months = 2
Average over 1 month = 2/3
Average over 2 months = 4/3 = λ
More than four heavy rainfalls means 5, 6, 7,…
P(5) = (e^-λ x λ^5)/5! = 0.009257
P(6) = 0.002057
P(7) = 0.000392
P(8) = 0.000065
P(9) = 0.000010
P(10) = 0.000001
P(more than 4 heavy storms) = 0.01178 (4sf)