GATE CE 2026 Set 1 — Question 55
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Engineering Mathematics → Hydrographs & Groundwater → Binomial Distribution
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Question
A bridge with an expected life of 50 years is designed for a flood of corresponding to the return period of 100 years. The risk associated with this design is _____________ (rounded off to two decimal places).
Correct answer
0.38 to 0.41
Solution
Risk is defined as the probability that a design event (with a return period ) will occur at least once during the expected life () of the structure.
The risk is the complement of this probability:
Rounding to two decimal places, the risk is .
1.Identify the given parameters:
- Expected life, years
- Return period, years
3.Calculate the annual probability of non-occurrence ():
4.Calculate the Risk ():
The probability that the event does not occur in years is .The risk is the complement of this probability:
5.Compute the numerical value:
Rounding to two decimal places, the risk is .
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