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?

검증된 단계별 안내

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.

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.

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.

Simplify the expression \( (0.8)^4 \) to find the probability. This involves raising 0.8 to the power of 4.

Interpret the result as the likelihood of no flooding occurring over the span of four consecutive years based on the given probability.

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

영상 길이:

주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

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.