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The probability that a hundred year flood may not occur at all during the 50 year life of the project is
  • a)
    0.395
  • b)
    0.990
  • c)
    0.605
  • d)
    0.133
Correct answer is option 'C'. Can you explain this answer?
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Given data:
Probability of occurrence of 100-year flood in 1 year = 1/100 = 0.01
Number of years in the life of the project = 50

To find: Probability that a hundred-year flood may not occur at all during the 50 year life of the project

Calculation:
Let P be the probability that a hundred-year flood may not occur in a given year.
Then, the probability that a hundred-year flood may not occur at all during the 50 year life of the project is given by:

P (no flood in 50 years) = P (no flood in year 1) × P (no flood in year 2) × … × P (no flood in year 50)

Since the floods in different years are independent events, we can multiply the probabilities of no flood in each year to get the probability of no flood in 50 years.

P (no flood in 50 years) = (1 - P (flood in year 1)) × (1 - P (flood in year 2)) × … × (1 - P (flood in year 50))

Substituting P (flood in a year) = 0.01, we get

P (no flood in 50 years) = (1 - 0.01) × (1 - 0.01) × … × (1 - 0.01) (50 times)
= 0.99 × 0.99 × … × 0.99 (50 times)

So, the required probability is 0.605 or 60.5%.

Therefore, option (c) is the correct answer.
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