Births in the United States In the United States, the true probability of a baby being a boy is 0.512 (based on the data available at this writing). For a family having three children, find the following.

d. The probability that at least one of the children is a girl.

검증된 단계별 안내

Step 1: Understand the problem. We are tasked with finding the probability that at least one of the three children in a family is a girl. The complement of this event is that all three children are boys. We will use the complement rule to solve this problem.

Step 2: Define the complement event. The complement event is that all three children are boys. The probability of a child being a boy is given as 0.512. Therefore, the probability of all three children being boys is the product of the probabilities for each child being a boy: P(All boys) = 0.512 × 0.512 × 0.512.

Step 3: Use the complement rule. The complement rule states that the probability of at least one girl is equal to 1 minus the probability of all boys. Mathematically, this is expressed as P(At least one girl) = 1 - P(All boys).

Step 4: Substitute the value of P(All boys) into the complement formula. Replace P(All boys) with the value calculated in Step 2 to find P(At least one girl).

Step 5: Interpret the result. The final value of P(At least one girl) represents the likelihood that at least one of the three children in the family is a girl. This is the desired 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. In this context, the probability of a baby being a boy is given as 0.512, which implies that the probability of a baby being a girl is 1 - 0.512 = 0.488. Understanding these basic probabilities is essential for calculating the likelihood of various outcomes in a family with three children.

Complementary Events

Complementary events are pairs of outcomes that cover all possible scenarios of a given situation. In this case, the event of having at least one girl is the complement of having no girls at all. By calculating the probability of the complementary event (having all boys), we can easily find the probability of having at least one girl by subtracting this value from 1.

Binomial Probability

Binomial probability refers to the probability of obtaining a fixed number of successes in a fixed number of independent Bernoulli trials. In this scenario, each child can be considered a trial with two outcomes (boy or girl). The binomial formula can be used to calculate the probability of having a specific number of boys or girls among the three children, which is crucial for determining the probability of having at least one girl.

Births in the United States In the United States, the true probability of a baby being a boy is 0.512 (based on the data available at this writing). For a family having three children, find the following.d. The probability that at least one of the children is a girl.