Answer the following questions for autosomal conditions such as PKU.
Parents who are each heterozygous carriers for a recessive mutant allele have a child who does not have the condition. What is the chance this child is a heterozygous carrier of the condition?

Verified step by step guidance

1. Identify the genotype of the parents: Since both parents are heterozygous carriers for a recessive mutant allele, their genotypes can be represented as $Aa$, where $A$ is the normal allele and $a$ is the recessive mutant allele.
2. Determine the possible genotypes of their child using a Punnett square: The possible genotypes are $AA$ (homozygous normal), $Aa$ (heterozygous carrier), and $aa$ (affected with the condition). The expected genotypic ratio is 1 $AA$ : 2 $Aa$ : 1 $aa$.
3. Since the child does not have the condition, exclude the $aa$ genotype from consideration. This leaves the possible genotypes for the child as either $AA$ or $Aa$.
4. Calculate the conditional probability that the child is a heterozygous carrier ($Aa$) given that the child is not affected. Use the formula: $\backslash text\{Probability\}\; =\; \backslash frac\{\backslash text\{Number\; of\; \}\; Aa\; \backslash text\{\; genotypes\}\}\{\backslash text\{Number\; of\; \}\; AA\; +\; Aa\; \backslash text\{\; genotypes\}\}$.
5. Substitute the values from the Punnett square into the formula to find the chance that the child is a heterozygous carrier given they do not have the condition.

Key Concepts

Autosomal Recessive Inheritance

Autosomal recessive inheritance means a condition manifests only when an individual inherits two copies of a mutant allele, one from each parent. Carriers have one normal and one mutant allele but typically do not show symptoms. Understanding this pattern helps predict the likelihood of offspring being affected or carriers.

Genotype Probabilities in Carrier Parents

When both parents are heterozygous carriers, each child has a 25% chance of being affected (homozygous recessive), 50% chance of being a carrier (heterozygous), and 25% chance of being unaffected and not a carrier (homozygous dominant). These probabilities are derived from a Punnett square analysis.

Conditional Probability Given Phenotype

If a child does not have the condition (is unaffected), the probability that the child is a carrier changes because the affected genotype is excluded. This requires calculating the conditional probability of being heterozygous given the child is not affected, adjusting the original genotype probabilities accordingly.