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A 1-h rainfall of 10 cm magnitude at a station has a return period of 50 years. The probability that a 1-h rainfall of magnitude 10 cm or more will occur in each of two successive years is:
- a)0.04
- b)0.2
- c)0.02
- d)0.0004
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
A 1-h rainfall of 10 cm magnitude at a station has a return period of ...
Given:
- 1-h rainfall of magnitude 10 cm has a return period of 50 years.
To find:
- Probability of a 1-h rainfall of magnitude 10 cm or more occurring in each of two successive years.
Solution:
1. Return period: The return period (T) is the average time interval between occurrences of a particular rainfall magnitude or event. It can be calculated as:
T = (n+1) / m
where,
n = number of years of record
m = rank of the rainfall magnitude
For a 1-h rainfall of 10 cm magnitude with a return period of 50 years, we can calculate the rank (m) as:
m = (n+1) / T
m = (50+1) / 1
m = 51
2. Probability of occurrence: The probability (P) of an event occurring in any given year can be calculated as:
P = 1 / T
where,
T = return period
For a 1-h rainfall of 10 cm magnitude with a return period of 50 years, the probability of occurrence (P) in any given year is:
P = 1 / 50
P = 0.02
3. Probability of occurrence in two successive years: The probability of the same event occurring in two successive years can be calculated as:
P2 = P * P = (1 / T) * (1 / T) = 1 / T^2
For a 1-h rainfall of 10 cm magnitude with a return period of 50 years, the probability of occurrence in two successive years (P2) is:
P2 = 1 / (50^2)
P2 = 0.0004
Therefore, the correct answer is option 'D' (0.0004).
- 1-h rainfall of magnitude 10 cm has a return period of 50 years.
To find:
- Probability of a 1-h rainfall of magnitude 10 cm or more occurring in each of two successive years.
Solution:
1. Return period: The return period (T) is the average time interval between occurrences of a particular rainfall magnitude or event. It can be calculated as:
T = (n+1) / m
where,
n = number of years of record
m = rank of the rainfall magnitude
For a 1-h rainfall of 10 cm magnitude with a return period of 50 years, we can calculate the rank (m) as:
m = (n+1) / T
m = (50+1) / 1
m = 51
2. Probability of occurrence: The probability (P) of an event occurring in any given year can be calculated as:
P = 1 / T
where,
T = return period
For a 1-h rainfall of 10 cm magnitude with a return period of 50 years, the probability of occurrence (P) in any given year is:
P = 1 / 50
P = 0.02
3. Probability of occurrence in two successive years: The probability of the same event occurring in two successive years can be calculated as:
P2 = P * P = (1 / T) * (1 / T) = 1 / T^2
For a 1-h rainfall of 10 cm magnitude with a return period of 50 years, the probability of occurrence in two successive years (P2) is:
P2 = 1 / (50^2)
P2 = 0.0004
Therefore, the correct answer is option 'D' (0.0004).
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Community Answer
A 1-h rainfall of 10 cm magnitude at a station has a return period of ...
Return period of rainfall,
T & = 50 years
∴ probability of occurrence once in 50 years,
p & = (1/50) & = 0.02
Probability of occurrence in each of 2 successive year = p2 = (0.02)2 = 0.0004.
T & = 50 years
∴ probability of occurrence once in 50 years,
p & = (1/50) & = 0.02
Probability of occurrence in each of 2 successive year = p2 = (0.02)2 = 0.0004.
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A 1-h rainfall of 10 cm magnitude at a station has a return period of 50 years. The probability that a 1-h rainfall of magnitude 10 cm or more will occur in each of two successive years is:a)0.04b)0.2c)0.02d)0.0004Correct answer is option 'D'. Can you explain this answer?
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A 1-h rainfall of 10 cm magnitude at a station has a return period of 50 years. The probability that a 1-h rainfall of magnitude 10 cm or more will occur in each of two successive years is:a)0.04b)0.2c)0.02d)0.0004Correct answer is option 'D'. Can you explain this answer? for Civil Engineering (CE) 2024 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about A 1-h rainfall of 10 cm magnitude at a station has a return period of 50 years. The probability that a 1-h rainfall of magnitude 10 cm or more will occur in each of two successive years is:a)0.04b)0.2c)0.02d)0.0004Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A 1-h rainfall of 10 cm magnitude at a station has a return period of 50 years. The probability that a 1-h rainfall of magnitude 10 cm or more will occur in each of two successive years is:a)0.04b)0.2c)0.02d)0.0004Correct answer is option 'D'. Can you explain this answer?.
A 1-h rainfall of 10 cm magnitude at a station has a return period of 50 years. The probability that a 1-h rainfall of magnitude 10 cm or more will occur in each of two successive years is:a)0.04b)0.2c)0.02d)0.0004Correct answer is option 'D'. Can you explain this answer? for Civil Engineering (CE) 2024 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about A 1-h rainfall of 10 cm magnitude at a station has a return period of 50 years. The probability that a 1-h rainfall of magnitude 10 cm or more will occur in each of two successive years is:a)0.04b)0.2c)0.02d)0.0004Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A 1-h rainfall of 10 cm magnitude at a station has a return period of 50 years. The probability that a 1-h rainfall of magnitude 10 cm or more will occur in each of two successive years is:a)0.04b)0.2c)0.02d)0.0004Correct answer is option 'D'. Can you explain this answer?.
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A 1-h rainfall of 10 cm magnitude at a station has a return period of 50 years. The probability that a 1-h rainfall of magnitude 10 cm or more will occur in each of two successive years is:a)0.04b)0.2c)0.02d)0.0004Correct answer is option 'D'. Can you explain this answer?, a detailed solution for A 1-h rainfall of 10 cm magnitude at a station has a return period of 50 years. The probability that a 1-h rainfall of magnitude 10 cm or more will occur in each of two successive years is:a)0.04b)0.2c)0.02d)0.0004Correct answer is option 'D'. Can you explain this answer? has been provided alongside types of A 1-h rainfall of 10 cm magnitude at a station has a return period of 50 years. The probability that a 1-h rainfall of magnitude 10 cm or more will occur in each of two successive years is:a)0.04b)0.2c)0.02d)0.0004Correct answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
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