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?

Verified step by step guidance

1. Identify the probability of no flooding in a single year. Since the probability of flooding in a year is 0.2, the probability of no flooding in a single year is calculated as 1 - 0.2 = 0.8.
2. Understand that the problem involves consecutive years, which means the events are independent. The probability of no flooding for four consecutive years is the product of the probabilities of no flooding in each year.
3. Express the probability of no flooding for four consecutive years mathematically as \( P = (0.8)^4 \). This uses the rule of multiplying probabilities for independent events.
4. Simplify the expression \( (0.8)^4 \) to find the probability. This involves raising 0.8 to the power of 4.
5. Interpret the result as the likelihood of no flooding occurring over the span of four consecutive years based on the given probability.

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.