A 6-hour rainfall of 6 cm at a place A was found to have a return period of 40 years. The probability that a 6 hour rainfall of this or larger magnitude will occur at least once in 20 successive years is:

Question

Question

This question was previously asked in

DFCCIL Executive Civil Official Paper (Held On: 10 Nov, 2018 Shift 2)

Answer 1

Concept:

Return Period (T): It is the average time interval between the occurrence of rainfall of magnitude equal to or in excess of a specific magnitude.
Probability (P): The probability of rainfall whose magnitude is equal to or in excess of specific magnitude having a return period of T is given as, \(\text{P} = \frac{1}{T}\)
q = probability of rainfall not occurring in a given year = 1 - P
Probability of rainfall not occurring at all in 'n' successive years = qⁿ
Probability of rainfall occurring at least once in 'n' successive years = 1 - qⁿ

Calculation:

Given,

n = 20 years, T = 40 years

∵ We know that, \(\text{P} = \frac{1}{T}\)

⇒ \(\text{P} = \frac{1}{40}\) = 0.025

∴ q = 1 - P = 0.975

∵ We know that the Probability of rainfall occurring at least once in 'n' successive years = 1 - qn

⇒ Probability of rainfall occurring at least once in '20' successive years = 1 - 0.975²⁰ = 0.397