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The probability that the annual maximum flood discharge will exceed 25000 m3/s, at least once in next 5 years is found to be 0.25. The return period of this flood event (in years, round off to 1 decimal place) is ____
- a)12.2
- b)16.4
- c)17.9
- d)20.6
Correct answer is option 'C'. Can you explain this answer?
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The probability that the annual maximum flood discharge will exceed 25...
Given:
- Probability of annual maximum flood discharge exceeding 25000 m3/s at least once in the next 5 years is 0.25.
To find:
- The return period of this flood event in years.
Return Period:
The return period is a measure of the average time between occurrences of an event of a given magnitude. It is calculated using the formula:
Return period = (n + 1) / (m + 1)
Where,
n = number of years in the record
m = rank of the event
Solution:
In this case, the probability of the flood event occurring in the next 5 years is given as 0.25. So, the probability of the event not occurring in the next 5 years is 1 - 0.25 = 0.75.
Probability of no occurrence in 5 years:
The probability of the event not occurring in 5 years is given by the product of the probabilities of no occurrence in each year:
P(no occurrence in 5 years) = (0.75)^5 = 0.2373
Probability of at least one occurrence in 5 years:
The probability of at least one occurrence in 5 years is the complement of the probability of no occurrence:
P(at least one occurrence in 5 years) = 1 - P(no occurrence in 5 years) = 1 - 0.2373 = 0.7627
Return period:
Using the formula for return period, we can calculate the return period for this event:
Return period = (n + 1) / (m + 1)
Here, n = 5 (number of years in the record) and the probability of at least one occurrence in 5 years is 0.7627.
Return period = (5 + 1) / (0.7627 + 1) = 6 / 1.7627 = 3.4 years
Therefore, the return period of this flood event is approximately 3.4 years, which rounded off to 1 decimal place is 3.4 years. However, none of the given options match this result.
Hence, the correct answer cannot be determined from the given options.
- Probability of annual maximum flood discharge exceeding 25000 m3/s at least once in the next 5 years is 0.25.
To find:
- The return period of this flood event in years.
Return Period:
The return period is a measure of the average time between occurrences of an event of a given magnitude. It is calculated using the formula:
Return period = (n + 1) / (m + 1)
Where,
n = number of years in the record
m = rank of the event
Solution:
In this case, the probability of the flood event occurring in the next 5 years is given as 0.25. So, the probability of the event not occurring in the next 5 years is 1 - 0.25 = 0.75.
Probability of no occurrence in 5 years:
The probability of the event not occurring in 5 years is given by the product of the probabilities of no occurrence in each year:
P(no occurrence in 5 years) = (0.75)^5 = 0.2373
Probability of at least one occurrence in 5 years:
The probability of at least one occurrence in 5 years is the complement of the probability of no occurrence:
P(at least one occurrence in 5 years) = 1 - P(no occurrence in 5 years) = 1 - 0.2373 = 0.7627
Return period:
Using the formula for return period, we can calculate the return period for this event:
Return period = (n + 1) / (m + 1)
Here, n = 5 (number of years in the record) and the probability of at least one occurrence in 5 years is 0.7627.
Return period = (5 + 1) / (0.7627 + 1) = 6 / 1.7627 = 3.4 years
Therefore, the return period of this flood event is approximately 3.4 years, which rounded off to 1 decimal place is 3.4 years. However, none of the given options match this result.
Hence, the correct answer cannot be determined from the given options.
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The probability that the annual maximum flood discharge will exceed 25000 m3/s,at least once in next 5 years is found to be 0.25. The return period of this flood event (in years, round off to 1 decimal place) is ____a)12.2b)16.4c)17.9d)20.6Correct answer is option 'C'. Can you explain this answer?
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