The probability that there are fewer than 3 tornadoes in a 14-year period is 0.9923.
Since the number of tornados in any year is independent of the number of tornados in any other year, the probability of fewer than 3 tornados in a 14-year period is the product of the probabilities of fewer than 3 tornados in each individual year.
The probability of no tornadoes in a year is 1 - 0.03 = 0.97.
The probability of 1 or 2 tornados can be calculated using the binomial probability formula.
The probability of 1 tornado is:
P(1 tornado) = 14C1 * 0.03^1 * 0.97^13 = 0.3248
The probability of 2 tornados is:
P(2 tornados) = 14C2 * 0.03^2 * 0.97^12 = 0.0598
Therefore, the probability of fewer than 3 tornados in a year is:
P(fewer than 3 tornados) = P(0 tornadoes) + P(1 tornado) + P(2 tornados) = 0.97^14 + 14C1 * 0.03^1 * 0.97^13 + 14C2 * 0.03^2 * 0.97^12 = 0.9923
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.