Answer to Question #304637 in Statistics and Probability for bnh

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 0.02.

• 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 14-year period.

Answer 1

Let $X=$ the number of tornados: $X\sim Bin(n, p).$

Given $n=14, p=0.02, q=0.98.$

$$P(X<3)=P(X=0)+P(X=1)+P(X=2)$$

$$=\dbinom{14}{0}(0.02)^0(0.98)^{14-0}+\dbinom{14}{1}(0.02)^1(0.98)^{14-1}$$

$$+\dbinom{14}{2}(0.02)^2(0.98)^{14-2}=0.75364194147$$

$$+0.21532626899+0.02856368874$$

$$=0.99753189921$$