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

Answer

Given, Probability of a tornado in any calendar year = 0.01

Therefore, Probability of no – tornado in any calendar year = 1 – 0.01 = 0.99

And it is also given that there can be at most one tornado in any calendar year and the number of tornadoes in any calendar year is independent of the number of tornados in any other calendar year.

Let X be a random variable representing the number of tornadoes in a 16 – year period

Therefore, X follows Binomial Distribution with parameters, n = 16 and p (probability of a tornado) = 0.01

The P. M. F. of X, f(x) = (nCx).(p^x).(1 - p)^(n - x)    x = 0, 1, 2, …,n

According to the problem,

The required probability, Prob.[X < 3] = P[X = 2] + P[X = 1] + P[X = 0]

                                                 = [(16C2) x (0.01^2) x (0.99)^14] + [(16C1) x (0.01^1) x (0.99)^15] + [(16C0) x (0.01^0) x (0.99)^16]

                                           = 0.9995 (rounded up to 4 decimal places)

Therefore, Probability that there are fewer than 3 tornadoes in a 16 – year period is 0.9995