Correct Answer - Option 1 : 36.6%
Explanation
The probability for the annual maximum flood magnitude to occur (p) = \(\frac{1}{{Return\;period\;}} = \frac{1}{{100}}\)
The probability of non-occurrence = 1 - p = 99/100
The probability of occurrence of an event will happen exactly r no. of times
\({\rm{p}} = {{\rm{n}}_{{{\rm{c}}_{\rm{r}}}}}{{\rm{p}}^{\rm{r}}}{\left( {1 - {\rm{p}}} \right)^{{\rm{n}} - {\rm{r}}}}\)
∴ The probability that the above flood magnitude will be not occurring during the next 100 years will be
i.e. r = 0, n = 100
P = 100C0 × p0 × q100
P = 1 × 1 × (99/100)100
P = 0.366 = 36.6 %
∴ percentage chance of a flood with the 100-year frequency of not occurring in the coming 100 years is 36.6%
