A male and a female are each heterozygous for both cystic fibrosis (CF) and phenylketonuria (PKU). Both conditions are autosomal recessive, and they assort independently.
What proportion of the children will be carriers of one or both conditions?

Verified step by step guidance

1. Identify the genotypes of the parents for both traits. Since both are heterozygous for cystic fibrosis (CF) and phenylketonuria (PKU), their genotypes can be represented as $Cc$ for CF and $Pp$ for PKU, where uppercase letters represent the dominant (normal) alleles and lowercase letters represent the recessive (disease) alleles.
2. Determine the possible gametes each parent can produce. Because the genes assort independently, each parent can produce four types of gametes: $C\; P$, $C\; p$, $c\; P$, and $c\; p$, each with equal probability (1/4).
3. Construct a Punnett square combining the gametes from both parents to find the genotypic combinations of their children. This will result in 16 possible genotype combinations, each with a probability of 1/16.
4. Classify each genotype according to whether the child is a carrier for CF, PKU, both, or neither. A carrier is heterozygous for the trait (e.g., $C\; c$ for CF or $P\; p$ for PKU). Children who are homozygous dominant or homozygous recessive for either trait are not carriers for that trait.
5. Calculate the proportion of children who are carriers of one or both conditions by summing the probabilities of genotypes that are heterozygous for CF, PKU, or both. Use the Punnett square results to identify these genotypes and add their probabilities accordingly.

Key Concepts

Autosomal Recessive Inheritance

Autosomal recessive traits require two copies of the mutant allele for the phenotype to be expressed. Carriers have one normal and one mutant allele but do not show symptoms. Understanding this helps determine the genotypes and phenotypes of offspring when both parents are heterozygous carriers.

Independent Assortment

Independent assortment means that alleles of different genes segregate independently during gamete formation. This principle allows the calculation of combined probabilities for inheriting alleles of two different genes, such as CF and PKU, by multiplying their individual probabilities.

Carrier Probability Calculation

Calculating the proportion of carriers involves determining the likelihood that offspring inherit one mutant allele for either or both conditions. This requires using Punnett squares or probability rules to find the chance of being heterozygous for CF, PKU, or both, excluding affected or non-carrier genotypes.