Question

A 1-h rainfall of 10 cm magnitude at a station has a return period of 50 years. The probability that a 1-h rainfall of magnitude 10 cm or more will occur in each of two successive years is:

• A. 0.04
• B. 0.2
• C. 0.02
• D. 0.0004

Answer 1

The correct option is D 0.0004

Given data: 1 hr, 10 cm rainfall has a return period of 50 years i.e. T = 50 yrs.

The probability of occurrence of an event, r times in 'n' successive years
=${}^n{C}_r{P}^r{q}^{n-r}$
Where,
P = probability of occurrence of
an event
$=\left(\frac{1}{T}\right)$
q = probability of non-occurrence
$=1-\left(\frac{1}{T}\right)$

Probability of occurrence of 1hr, 10 cm rainfall or more, occurring in each of two successive years
$={}^2{C}_2{p}^2{q}^{2-2}$
$={}^2{C}_2{p}^2{q}^0$
$=1\times {\left(\frac{1}{50}\right)}^2\times 1=0.0004$