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A 2-h rainfall of 5 cm magnitude at a station has a return period of 10 years. The probability that a 2-h rainfall of magnitude 5 cm or more will occur in each of three successive years is____ ( rounded off to three decimal places)
Correct answer is '0.001'. Can you explain this answer?
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A 2-h rainfall of 5 cm magnitude at a station has a return period of ...
Given information:
- 2-h rainfall of 5 cm magnitude at a station has a return period of 10 years.
To find:
- Probability that a 2-h rainfall of magnitude 5 cm or more will occur in each of three successive years.
Solution:
1. Calculation of annual probability of occurrence of 2-h rainfall of 5 cm magnitude:
- Using the formula for return period (T), we can find the annual probability (P) of occurrence of a rainfall event of a given magnitude:
T = 1/P
P = 1/T
- Given return period (T) = 10 years
P = 1/10 = 0.1 = 10%
2. Calculation of probability of occurrence of 2-h rainfall of 5 cm or more in three successive years:
- Assuming that each year's rainfall is independent of the previous year's rainfall, the probability of occurrence of a 2-h rainfall of 5 cm or more in each of three successive years is the product of the individual annual probabilities:
P(3 years) = P * P * P
P(3 years) = 0.1 * 0.1 * 0.1 = 0.001
3. Final answer:
- The probability that a 2-h rainfall of magnitude 5 cm or more will occur in each of three successive years is 0.001 (rounded off to three decimal places).
- 2-h rainfall of 5 cm magnitude at a station has a return period of 10 years.
To find:
- Probability that a 2-h rainfall of magnitude 5 cm or more will occur in each of three successive years.
Solution:
1. Calculation of annual probability of occurrence of 2-h rainfall of 5 cm magnitude:
- Using the formula for return period (T), we can find the annual probability (P) of occurrence of a rainfall event of a given magnitude:
T = 1/P
P = 1/T
- Given return period (T) = 10 years
P = 1/10 = 0.1 = 10%
2. Calculation of probability of occurrence of 2-h rainfall of 5 cm or more in three successive years:
- Assuming that each year's rainfall is independent of the previous year's rainfall, the probability of occurrence of a 2-h rainfall of 5 cm or more in each of three successive years is the product of the individual annual probabilities:
P(3 years) = P * P * P
P(3 years) = 0.1 * 0.1 * 0.1 = 0.001
3. Final answer:
- The probability that a 2-h rainfall of magnitude 5 cm or more will occur in each of three successive years is 0.001 (rounded off to three decimal places).
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Community Answer
A 2-h rainfall of 5 cm magnitude at a station has a return period of ...
P = nCkPkQn–k
P = 3C3(1/10)3Q0
P = 0.001
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A 2-h rainfall of 5 cm magnitude at a station has a return period of 10 years. The probability that a 2-h rainfall of magnitude 5 cm or more will occur in each of three successive years is____ ( rounded off to three decimal places)Correct answer is '0.001'. Can you explain this answer?
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