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 0.15.
. 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 19 year period.

Answer 1

.441320612

or

44.132%

Explanation:

This is binomial

fewer than 3 is equal to p(0)+p(1)+p(2)

`p(0)={19\choose0}*.15^0*(1-.15)^(19)=.045599448\\p(1)={19\choose1}*.15^1*(1-.15)^(18)=.152892268\\p(2)={19\choose2}*.15^2*(1-.15)^(17)=.242828896\\p(0)+p(1)+p(2)=.441320612`