Answer the following questions for autosomal conditions such as PKU.
If the first child of parents who are both heterozygous carriers of a recessive mutant allele is homozygous recessive, what is the chance the second child of the couple will be homozygous recessive? What is the chance the second child will be a heterozygous carrier of the recessive mutation?

Verified step by step guidance

1. Identify the genotype of the parents: Since both parents are heterozygous carriers of 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 children using a Punnett square: Cross $Aa$ (mother) with $Aa$ (father) to find the genotypic ratio of offspring. The possible genotypes are $AA$, $Aa$, and $aa$.
3. Calculate the probability of the second child being homozygous recessive ($aa$): From the Punnett square, the chance of $aa$ is 1 out of 4, or 25%. This probability is independent of the first child's genotype because each child's genotype is an independent event.
4. Calculate the probability of the second child being a heterozygous carrier ($Aa$): From the Punnett square, the chance of $Aa$ is 2 out of 4, or 50%.
5. Summarize the results: The chance the second child is homozygous recessive is 25%, and the chance the second child is a heterozygous carrier is 50%, regardless of the first child's genotype.

Key Concepts

Autosomal Recessive Inheritance

Autosomal recessive inheritance occurs when a trait is expressed only if 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. For two heterozygous carriers, each child has a 25% chance of being affected, 50% chance of being a carrier, and 25% chance of being unaffected.

Independent Assortment and Probability in Genetics

Each child’s genotype is determined independently according to Mendelian genetics, meaning the outcome for one child does not affect the probabilities for the next. Thus, even if the first child is homozygous recessive, the chance for the second child to inherit the same genotype remains the same as the initial probability.

Genotype Probabilities for Offspring of Carrier Parents

When both parents are heterozygous carriers, the possible genotypes for each child are: 25% homozygous recessive (affected), 50% heterozygous carrier (unaffected but carrier), and 25% homozygous dominant (unaffected, non-carrier). These probabilities apply independently to each child regardless of previous offspring’s genotype.