Question

The probability of a tornado occurring in a subdivision in Tornado Alley in the United States has been estimated to be 0.2 for one occurrence, 0.03 for two occurrences, and 0.001 for three occurrences during the next 50 years. Assume that the chance of four or more occurrences is negligible during the next 50 years. If a tornado hits a structure, the probability that it will suffer damage is 70%. Assume that the damage from multiple tornadoes is statistically independent. What is the probability that a structure will not suffer any damage from tornadoes in the next 50 years

Answer 1

Probability is 0.831727

Explanation:

The probability can be calculated as below

There are multiple scenarios

Scanerio 1

0 occurance & No damage = 1 - 0.2 - 0.03 - 0.001 = 0.769

Scanerio 2

1 occurance & No damage = 0.2 x ( 1 - 0.7 ) = 0.06

Scanerio 3

2 occurance & No damage = 0.03 x ( 1 - 0.7 )^2 = 0.0027

Scanerio 4

3 occurance & No damage = 0.001 x ( 1 - 0.7 )^3 = 0.000027

P(structure will not suffer any damage) = Scanerio 1 + Scanerio 2 + Scanerio 3 + Scanerio 4 = 0.769 + 0.06 + 0.0027 + 0.000027 = 0.831727