Question

The probability that a storm event with a return period of 20 years will occur once in a 5-year period is \underline{\hspace{6cm}} (rounded off to 2 decimal places).

Hint:

Use the complement rule: Probability(at least one) = \(1 - \text{Probability(none)}\). This is the fastest way to solve return-period probability problems.

Answer 1

Step 1: Recall return period relation. Return period \(T\) is the reciprocal of the probability of occurrence in a single year: \[ P_{\text{annual}} = \frac{1}{T} \] For \(T = 20 \, \text{years}\): \[ P_{\text{annual}} = \frac{1}{20} = 0.05 \]

Step 2: Probability of non-occurrence in a year. \[ P_{\text{not, annual}} = 1 - 0.05 = 0.95 \]

Step 3: Probability of non-occurrence in 5 years. Since the years are independent: \[ P_{\text{not, 5 years}} = (0.95)^5 \] \[ = 0.77378 \; \text{(approx)} \]

Step 4: Probability of at least one occurrence. \[ P_{\text{at least one}} = 1 - P_{\text{not, 5 years}} \] \[ = 1 - 0.77378 = 0.2262 \] Rounded off to 2 decimal places: \[ \boxed{0.22} \]