Question

A company prices its tornado insurance using the following assumptions: • In any calendar year, there can be at most one tornado. • In any calendar year, the probability of a tornado is 0.05. • The number of tornadoes in any calendar year is independent of the number of tornados in any other calendar year. Using the company's assumptions, calculate the probability that there are fewer than 3 tornadoes in a 15-year period.

Answer 1

Let X = The number of tornadoes in the 15-year period.

The assumption of the company are as follow:

In any calendar year, there can be at most one tornado. So there are only two possible outcomes in a year as "zero tornado"

or "one tornado". So X takes values from 0 to 15

Also the number of tornadoes in any calendar year is independent of the number of tornados in any other calendar year.

The probability of  a tornado is 0.05 in a yea. Which is constant in every year.

So X follows binomial distribution with n = 15, p = 0.05

Here we want to find P( X < 3 ) = P(X <= 3 -1 ) = P(X <= 2)

Let's use excel:

P(X <= 2) = "=BINOMDIST(2,15,0.05,1)" = 0.9638

So the probability that there are fewer than 3 tornadoes in a 15-year period is 0.9638.