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A hydraulic structure has been designed for a 50 year flood. The probability that exactly one flood of the design capacity will occur in the 75 year life of the structure is
- a)0.02
- b)0.220
- c)0.336
- d)0.780
Correct answer is option 'C'. Can you explain this answer?
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A hydraulic structure has been designed for a 50 year flood. The proba...
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A hydraulic structure has been designed for a 50 year flood. The proba...
Solution:
Given: Probability of design capacity flood in 50 years = 1/50
We need to find the probability of exactly one flood of design capacity in the 75-year life of the structure.
To solve the problem, we can use the Poisson distribution formula, which gives the probability of a certain number of events occurring in a fixed interval of time, given the average rate of occurrence.
The formula is:
P(X=k) = (e^(-λ) * λ^k) / k!
where X is the random variable representing the number of events, k is the number of events we want to find the probability for, λ is the average rate of occurrence, and e is the base of the natural logarithm.
Let's calculate the value of λ first:
The expected number of design capacity floods in 75 years is:
λ = (75 / 50) * 1 = 1.5
Now, let's use the Poisson distribution formula to find the probability of exactly one flood of design capacity in 75 years:
P(X=1) = (e^(-1.5) * 1.5^1) / 1! = 0.336
Therefore, the answer is (c) 0.336, which is option (c).
Given: Probability of design capacity flood in 50 years = 1/50
We need to find the probability of exactly one flood of design capacity in the 75-year life of the structure.
To solve the problem, we can use the Poisson distribution formula, which gives the probability of a certain number of events occurring in a fixed interval of time, given the average rate of occurrence.
The formula is:
P(X=k) = (e^(-λ) * λ^k) / k!
where X is the random variable representing the number of events, k is the number of events we want to find the probability for, λ is the average rate of occurrence, and e is the base of the natural logarithm.
Let's calculate the value of λ first:
The expected number of design capacity floods in 75 years is:
λ = (75 / 50) * 1 = 1.5
Now, let's use the Poisson distribution formula to find the probability of exactly one flood of design capacity in 75 years:
P(X=1) = (e^(-1.5) * 1.5^1) / 1! = 0.336
Therefore, the answer is (c) 0.336, which is option (c).
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A hydraulic structure has been designed for a 50 year flood. The probability that exactly one flood of the design capacity will occur in the 75 year life of the structure isa)0.02b)0.220c)0.336d)0.780Correct answer is option 'C'. Can you explain this answer?
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A hydraulic structure has been designed for a 50 year flood. The probability that exactly one flood of the design capacity will occur in the 75 year life of the structure isa)0.02b)0.220c)0.336d)0.780Correct answer is option 'C'. Can you explain this answer? for Civil Engineering (CE) 2025 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 hydraulic structure has been designed for a 50 year flood. The probability that exactly one flood of the design capacity will occur in the 75 year life of the structure isa)0.02b)0.220c)0.336d)0.780Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A hydraulic structure has been designed for a 50 year flood. The probability that exactly one flood of the design capacity will occur in the 75 year life of the structure isa)0.02b)0.220c)0.336d)0.780Correct answer is option 'C'. Can you explain this answer?.
A hydraulic structure has been designed for a 50 year flood. The probability that exactly one flood of the design capacity will occur in the 75 year life of the structure isa)0.02b)0.220c)0.336d)0.780Correct answer is option 'C'. Can you explain this answer? for Civil Engineering (CE) 2025 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 hydraulic structure has been designed for a 50 year flood. The probability that exactly one flood of the design capacity will occur in the 75 year life of the structure isa)0.02b)0.220c)0.336d)0.780Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A hydraulic structure has been designed for a 50 year flood. The probability that exactly one flood of the design capacity will occur in the 75 year life of the structure isa)0.02b)0.220c)0.336d)0.780Correct answer is option 'C'. Can you explain this answer?.
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