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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 0.12.

• 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 11-year period. Give your answer as a fraction or decimal out to at least 4 places.

Answer 1

This is Binomial distribution: only two outcomes each year, 1 tornado or 0 tornadoes, and so on.

p = 0.12 (probability of "success" i.e. having a tornado that year)

n = 11 trials i.e. years.

X = number of tornadoes in 11 years

possible values of X = 0, 1, 2, 3, ....., 11

Find P(X < 3) = P(0) + P(1) + P(2), which will be your answer.

You can use any Binomial calculator or calculate each term by hand, using formulas, and add them up.