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 0.08.
• 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 2 tornadoes in a 11-year period.

Answer 1

Answer :

Given that :

The probability of a tornado = 0.08.

The number of tornadoes in any calendar year is independent

Already we know that :

the binomial distribution of p is as follows :

Given population proportion of success p = 0.08

q = 1 - p

= 1 - 0.08

q = 0.92

and given sample size n = 11

so we need to calculate Pr(x<2)

consider Pr(x<2) = Pr(x = 0) + Pr(x = 1)

now substitute the values in above formula :

Therefore the probability of fewer than 2 tornadoes in 11 years = 0.78189