Question

The number of tornadoes in a county during a year is modeled with the following assumptions: In a calendar year, the number of tornadoes is binomial with n = 2 and p = 0.01.The number of tornadoes in any year is independent of any other year.Under these assumptions, calculate the probability the county will experience exactly 2 tornadoes in a ten-year period.

Answer 1

0.0041 is the probability the county will experience exactly 2 tornadoes in a ten-year period.

Explanation:

We are given the following information:

We treat occurrence of tornado as a success.

P(Tornado) = 0.01

Then the number of adults follows a binomial distribution, where

`P(X=x) = \binom{n}{x}.p^x.(1-p)^(n-x)`

where n is the total number of observations, x is the number of success, p is the probability of success.

Now, we are given n = 10 and x = 2

We have to evaluate:

`P(x = 2)\\= \binom{10}{2}(0.01)^2(1-0.01)^8\\= 0.0041`

0.0041 is the probability the county will experience exactly 2 tornadoes in a ten-year period.