Parents both have unattached earlobes, but some of their children have attached earlobes. Explain, in terms of phenotype and genotype. (pages \(466-67\) )

Phenotype is the physical appearance or observable traits of an individual. In this case, the phenotypes are unattached earlobes (dominant trait) and attached earlobes (recessive trait). Genotype is the combination of alleles (genetic information) that determines the phenotype. For earlobes, we can denote the dominant allele as \(E\) and the recessive allele as \(e\). An individual can have three possible genotypes: \(EE\), \(Ee\), and \(ee\). The genotypes \(EE\) and \(Ee\) will result in unattached earlobes (dominant), while the genotype \(ee\) will result in attached earlobes (recessive).

Since both parents have unattached earlobes, we know that their genotypes must be either \(EE\) or \(Ee\). Since their children can have attached earlobes, at least one parent must be heterozygous (\(Ee\)). Therefore, the parents' genotypes are either \(EE\) and \(Ee\) or both \(Ee\).

We will use Punnett squares to determine the probabilities of the children's genotypes. There are two scenarios to consider: Scenario 1: Parent 1 is \(EE\) and Parent 2 is \(Ee\). \[ \begin{array}{c || c | c} & E & e \\ \hline \hline E & EE & Ee \\ \hline E & EE & Ee \end{array} \] In this scenario, 100% of the children will have unattached earlobes, so this does not match our exercise description. Scenario 2: Both parents are \(Ee\). \[ \begin{array}{c || c | c} & E & e \\ \hline \hline E & EE & Ee \\ \hline e & Ee & ee \end{array} \] In this scenario, 75% of the children will have unattached earlobes (\(EE\) or \(Ee\)) and 25% will have attached earlobes (\(ee\)). This matches our exercise description.

The parents must both have the genotype \(Ee\) (heterozygous, carrying one dominant and one recessive allele) to produce children with attached earlobes. There will be a 25% chance for their children to have attached earlobes (\(ee\)) and a 75% chance to have unattached earlobes (\(EE\) or \(Ee\)).