Subtopic: Mean, median, mode and standard deviation
Question Statement:
The probability that a storm event with a return period of 20 years will occur once in 5-year period is ____________________(rounded off to 2 decimal places).
Official Answer Key:
0.19 to 0.21
Step-by-Step Solution & Explanation
Annual exceedance probability p = 1/T = 1/20 = 0.05. The number of occurrences in n=5 independent years follows a Binomial(n=5, p=0.05) distribution. P(exactly 1 occurrence in 5 years) = ⁵C₁×p¹×(1−p)⁴ = 5×0.05×0.95⁴ = 5×0.05×0.81450625 = 0.2036 ≈ 0.20. This lies within the official range 0.19–0.21.
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