The probability of a flood in any given year in a region prone to floods is 0.2. What is the probability of no flooding for four 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 flooding in a given year is 0.2, meaning there is a 20% chance of flooding.

Complementary Events

Complementary events are two outcomes of a probability experiment that are mutually exclusive and exhaustive. For instance, if the probability of flooding is 0.2, the probability of no flooding in a given year is the complement, calculated as 1 - 0.2 = 0.8. This concept is crucial for determining the likelihood of multiple consecutive events.

Independent Events

Independent events are those whose outcomes do not affect each other. In this scenario, the probability of no flooding in one year does not influence the probability in subsequent years. To find the probability of no flooding over multiple years, we multiply the probabilities of no flooding for each individual year, which is essential for solving the given problem.