Final answer:
Katie and George must both have the genotype Dd for cheek dimples, as their daughter Betsy does not have cheek dimples.
Step-by-step explanation:
To determine Katie and George's genotypes, we can use a Punnett square. Since their daughter Betsy does not have cheek dimples, it means that Betsy is homozygous recessive (dd) for this trait. To have a homozygous recessive offspring, both parents must contribute a recessive allele. Therefore, Katie and George must both have the genotype Dd for cheek dimples.
A Punnett square can be used to visually represent this. Let's use D to represent the dominant allele (cheek dimples) and d to represent the recessive allele (no cheek dimples). The Punnett square for a cross between two individuals with the genotype Dd would look like this:
DdDDDDddDddd
As we can see, there is a 25% chance (1 out of 4) of having an offspring with the genotype DD (homozygous dominant), a 50% chance (2 out of 4) of having an offspring with the genotype Dd (heterozygous), and a 25% chance (1 out of 4) of having an offspring with the genotype dd (homozygous recessive).