The probability of a flood in any given year in a region prone to floods is 0.2. What is the probability of a flood for three consecutive years?

Key Concepts

Probability Basics

Probability is a measure of the likelihood that an event will occur, expressed as a number between 0 and 1. A probability of 0 indicates an impossible event, while a probability of 1 indicates a certain event. In this context, the probability of a flood occurring in any given year is 0.2, meaning there is a 20% chance of a flood happening.

Independent Events

Independent events are those whose outcomes do not affect each other. In this scenario, the occurrence of a flood in one year does not influence the probability of a flood in the following years. Therefore, to find the probability of floods occurring over multiple years, we can multiply the probabilities of each individual event.

Multiplication Rule of Probability

The multiplication rule states that the probability of multiple independent events occurring together is the product of their individual probabilities. For three consecutive years with a flood probability of 0.2, the overall probability of floods in all three years is calculated as 0.2 * 0.2 * 0.2, which simplifies to 0.008 or 0.8%.