A company prices its hurricane insurance using the following assumptions:

1. In any calendar year, there can be at most one hurricane.
2. In any calendar year, the probability of a hurricane is 0.05.
3. The numbers of hurricanes in different calendar years are mutually independent.

Using the company’s assumptions, calculate the probability that there are fewer than 3 hurricanes in a 20-year period.

• 0.06
• 0.19
• 0.38
• 0.62
• 0.92

Copyright 2023. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.

Solution: E

Let X be the number of hurricanes over the 20-year period. The conditions of the problem give x is a binomial distribution with n = 20 and p = 0.05 . It follows that

P[X < 2] = (0.95)20(0.05)0 + 20(0.95)19(0.05) + 190(0.95)18(0.05)2 = 0.358 + 0.377 + 0.189 = 0.9245.