Two parents who are each known to be carriers of an autosomal recessive allele have four children. None of the children has the recessive condition. What is the probability that one or more of the children is a carrier of the recessive allele?

검증된 단계별 안내

Determine the genotype of the parents. Since both parents are carriers of an autosomal recessive allele, their genotypes are heterozygous (Aa).

Use a Punnett square to calculate the probabilities of the offspring's genotypes. Cross Aa (parent 1) with Aa (parent 2). The resulting genotypes are: 25% AA (homozygous dominant), 50% Aa (heterozygous carrier), and 25% aa (homozygous recessive).

Since none of the children has the recessive condition, the probability of each child being aa (homozygous recessive) is excluded. This means the possible genotypes for each child are either AA or Aa.

Calculate the probability of a child being a carrier (Aa). From the Punnett square, the probability of being Aa is 50%, and the probability of being AA is 50%. Since aa is excluded, the probabilities are normalized: P(Aa) = 50% / (50% + 50%) = 50%.

To find the probability that one or more of the four children is a carrier, use the complement rule. First, calculate the probability that none of the children is a carrier (all are AA). Then subtract this value from 1 to find the probability of at least one child being a carrier.

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주요 개념

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

Autosomal Recessive Inheritance

Autosomal recessive inheritance occurs when a trait or condition is expressed only when an individual has two copies of a recessive allele. Carriers, who possess one dominant and one recessive allele, do not exhibit the condition but can pass the recessive allele to their offspring. In this scenario, both parents are carriers, meaning each child has a chance of inheriting the recessive allele.

Punnett Square

A Punnett square is a diagram used to predict the genetic makeup of offspring from two parents. By arranging the alleles of each parent, it allows for the visualization of possible combinations in their children. In this case, a Punnett square can help determine the probabilities of the children being carriers or expressing the recessive condition.

Probability of Inheritance

The probability of inheritance refers to the likelihood that a specific genetic trait will be passed from parents to offspring. In the context of this question, it involves calculating the chances that at least one of the four children inherits the recessive allele from the carrier parents. This can be determined using the probabilities derived from the Punnett square.