SOLUTION: 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

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Question 1145776: 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 0.12.
• 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 4 tornadoes in a 17-year period.
Answer by VFBundy(438) About Me  (Show Source):
You can put this solution on YOUR website!
"Fewer than 4 tornadoes" is another way of saying 3,2,1, or 0 tornadoes.

Probability of exactly 3 tornadoes: %280.12%29%5E3%2A%280.88%29%5E14%2A%2817%21%2F%283%21%2A14%21%29%29 = 0.1963
Probability of exactly 2 tornadoes: %280.12%29%5E2%2A%280.88%29%5E15%2A%2817%21%2F%282%21%2A15%21%29%29 = 0.2878
Probability of exactly 1 tornado: %280.12%29%5E1%2A%280.88%29%5E16%2A%2817%21%2F%281%21%2A16%21%29%29 = 0.2638
Probability of exactly 0 tornadoes: %280.88%29%5E17 = 0.1138

Probability of "fewer than 4 tornadoes": 0.1963 + 0.2878 + 0.2638 + 0.1138 = 0.8617