A house you’re interested in buying would be affected by 20-year floods. What is the probability of that happening in any given year?

Understanding the Problem

To determine the probability of a house being affected by a 20-year flood in any given year, we need to interpret what a "20-year flood" means. A 20-year flood is defined as a flood event that has a 1 in 20 chance of occurring in any given year.

Relevant Concepts

The probability $P$ of an event occurring in any given timeframe can be represented mathematically as:

$P = \frac{1}{T}$

where $T$ is the return period (in this case, 20 years).

Detailed Analysis

1. Calculate the Probability: For a 20-year flood:

   $P = \frac{1}{20}$

2. Convert to Decimal: The probability in decimal form is:

   $P = 0.05$

3. Convert to Percentage: To express the probability as a percentage:

   $P = 0.05 \times 100 = 5\%$

Verify and Summarize

The calculation is straightforward and based on the definition of a 20-year flood. The annual probability of a 20-year flood occurring is correctly calculated as 5%.

Final Answer

The probability of a house being affected by a 20-year flood in any given year is 0.05, or 5%.