Question

The probability of a 10-year flood to occur at least once in the next 4 years is.........

• A. 25%
• B. 35%
• C. 50%
• D. 65%

Hint:

Use the formula \( P = 1 - (1 - \frac{1}{T})^n \) to calculate the probability of at least one occurrence of a flood or extreme event in a given number of years.

Answer 1

The Correct Option is B

The probability \( P \) of a 10-year flood (i.e., return period \( T = 10 \) years) occurring at least once in \( n = 4 \) years is given by: \[ P = 1 - (1 - \frac{1}{T})^n \] \[ P = 1 - \left(1 - \frac{1}{10}\right)^4 = 1 - (0.9)^4 = 1 - 0.6561 = 0.3439 \] \[ ⇒ P \approx 34.39% \approx \boxed{35%} \] Thus, the probability is 35%.