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 0.14.
• The number of tornadoes in any calendar year is independent of the number of tornadoes in any other calendar year.
Using the company's assumptions, calculate the probability that there are fewer than 2 tornadoes in a 12-year period.

In any calendar year, there can be at most one tornado. This means there can be either 1 tornado or 0 tornado i.e. there are only two possible outcomes of the event.

In any calendar year, the probability of a tornado is 0.14. This means, the probability of occurrence of an event is fixed. p = 0.14

The occurrence of tornado in one year is independent of the number of tornadoes in other years. This means the events are independent of each other.

We need to find the probability that there are fewer than 2 tornadoes in a 12-year period. This means the number of trials is fixed i.e. n = 12

All the conditions of a Binomial Experiment are being satisfied, so we will use Binomial Probability to solve this problem.

p = 0.14

q = 1 - p = 1 - 0.14 = 0.86

n = 12

x = 2

We need to find: P( x < 2)

Fewer than 2 tornadoes means either 1 or 0 tornado. So,

P(x < 2) = P(x=0) + P(x=1)

The formula of binomial probability is:

[tex]P(x)=^{n}C_{x}p^{x}q^{n-x}[/tex]

Using the formula for above expression, we get:

P(x < 2) = P(0) + P(1)

[tex]= ^{12}C_{0}(0.14)^{0}(0.86)^{(12-0)}+^{12}C_{1}(0.14)^{1}(0.86)^{(12-1)}\\\\ =0.1637 + 0.3197\\\\ =0.4834[/tex]

Therefore, the probability that there are fewer than 2 tornadoes in a 12-year period is 0.4834