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:

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 - PProbability of rainfall not occurring at all in 'n' successive years = qnProbability 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