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 0.03.
• 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 = number of tornados

n = 14

p = 0.03

here trials are independent and fixe, also there are only two possible outcomes with success probability is 0.03

so we can used binomial distribution to find the probability.

here we want to find P( X < 3) = P( X < = 3-1) = P(X <=2)

Using excel:

P( X <=2) = "=BINOMDIST(2,14,0.03,1)" = 0.992333

Note that the general command to find less than or equal binomial probability in excel is "=BINOMDIST(x, n, p, 1)"

So  the probability that there are fewer than 3 tornadoes in a 14-year period is 0.992333