What is the probability of a family having five boys born in a row? (Assume the probability of a male birth is 1/2.)

검증된 단계별 안내

Step 1: Understand the problem. The probability of a male birth is given as 1/2, and we are tasked with finding the probability of having five boys born consecutively. This involves multiplying probabilities for independent events.

Step 2: Recognize that each birth is an independent event. The probability of one boy being born does not affect the probability of the next boy being born.

Step 3: Write the probability for one boy being born as \( P(B) = \frac{1}{2} \). Since the events are independent, the probability of five boys being born consecutively is the product of the probabilities for each birth.

Step 4: Multiply the probabilities for five independent events: \( P(5 \text{ boys}) = \frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} \).

Step 5: Simplify the expression. The result will be \( \left( \frac{1}{2} \right)^5 \), which represents the probability of having five boys born in a row.

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. In this context, the probability of a single event, such as the birth of a boy, is given as 1/2. Understanding basic probability principles is essential for calculating the likelihood of multiple independent events occurring in sequence.

Independent Events

Independent events are those whose outcomes do not affect each other. In this scenario, the birth of each child is independent of the others, meaning the outcome of one birth does not influence the next. This concept is crucial for calculating the overall probability of multiple births resulting in boys, as it allows us to 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 this question, to find the probability of having five boys in a row, we multiply the probability of having a boy (1/2) by itself five times, resulting in (1/2)^5. This rule is fundamental for solving problems involving sequences of independent events.