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 0.01.

• 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 16-year period.

Answer 1

The 2nd and 3rd assumption matches with the binomial distribution assumption as the probability of each success is constant and the occurrence of every events is independent of others( here, occurrence of tornado in any year is independent of other year.

So, probability of occurrence of torando = probability of success= 0.01

Probability of not occurence of tornado= q= 1-p= 1-0.01= 0.99

So, probability of occurrence of fewer than 3 tornado on 16- year period is given by binomial distribution with n=16 ,p= 0.01 ,q= 0.99 and x= 0,1,2

P(X<3)= P(X=0)+P(X=1)+P(X=2)= (16c0)*.01^0*0.99^16 +(16c1)*0.01^1*0.99^15+ (16c2)*0.01^2*0.99^14=0.99949≈0.9995