Question

A particular community in the mid west experiences on average 3.0 tornadoes every year. What's the probability that the next tornado comes within the next 9 months

Answer 1

The probability that the next tornado comes within the next 9 months is 1-0.1054 = 0.8946

Explanation:

In 12 months the average of tornadoes is 3.0, does in 9 months, we can conclude, applying a rule of three, that the average of tornaoes is 3.0*9/12 = 2.25. We may assume that the distribution of Tornadoes is a period of time is Poisson. Lets call X the amount of Tornadoes in a 9 month period. X has distribution Poisson with parameter λ=2.25.

The probability that the next tornado comes within the next 9 months is equal to the probability of X being greater than or equal to 1. However P(X≥1) = 1-P(X=0), and

`P(X=0) = \frac{e^(-2.25)*{2.25}^(0)}{0!} = 0.1054`

Thus, the probability that the next tornado comes within the next 9 months is 1-0.1054 = 0.8946.