Answer to Question #188847 in Statistics and Probability for Amilaa

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 0.07. 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 20-year period

Answer 1

$n = 20 ,p = 0.07$

We need to find:

P(x < 3)

So, Probability of tornado fewer than 3-

$P(x < 2) = P(0) + P(1)+P(2)\\=^{20}C_0(0.1)^0 (0.93)^{20} +^{20}C_1(0.1)^1 (0.93)^{19} +^{20}C_2(0.1)^2 (0.93)^{18}$  

$=0.2342+0.3526+0.2521=0.839$