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steposvetlana [31]
3 years ago
7

The probability of a tornado occurring in a subdivision in Tornado Alley in the United States has been estimated to be 0.2 for o

ne 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
Mathematics
1 answer:
hoa [83]3 years ago
8 0

Answer:

Probability is 0.831727

Step-by-step 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

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<em />

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