Oompa Loompa Genetics: Oompahs can have red, blue, or purple hair. Purple hair comes from the heterozygous condition (recall Mendelian genetics complexities) results. In the land of Oompah, blue hair is highly valued. Blue-haired Oompahs ever get benefits. Oscar Oompah has purple hair, but he wants to find a wife that will specially give him blue-haired children. What color hair should his wife have? What would be his second choice? Wife with blue hair; second choice, wife with purple hair, first choice. Only a wife with red hair will give him blue-haired children, and this is the only choice he has. Wife with red hair; second choice, wife with purple hair, first choice. First choice, wife with purple hair; second choice, wife with red hair.
The Correct Answer and Explanation is:
Correct answer: First choice, wife with blue hair; second choice, wife with purple hair.
To understand this, we need to apply Mendelian genetics. There are three hair colors among the Oompahs: red, blue, and purple. The problem tells us that purple hair is the result of a heterozygous genotype. That means the purple-haired individuals carry two different alleles—one for red hair and one for blue hair. From this, we can infer that red and blue hair each arise from homozygous genotypes.
Let’s represent the alleles as follows:
- R = red allele
- B = blue allele
So:
- Red hair genotype: RR
- Blue hair genotype: BB
- Purple hair genotype: RB
Oscar Oompah has purple hair, so his genotype is RB. He wants to have children with blue hair, meaning the child must inherit one B allele from each parent. To achieve that, the mother must also provide a B allele.
A wife with blue hair must have the genotype BB. When crossed with Oscar’s RB, their offspring have a 50% chance of being BB (blue hair) and a 50% chance of being RB (purple hair). Therefore, this match gives the highest chance of producing blue-haired children.
A wife with purple hair (RB) also has one B allele. When crossed with Oscar’s RB, the probability of producing a BB child is 25%, as follows: 25% RR (red), 25% BB (blue), and 50% RB (purple). So this is the second-best option.
A wife with red hair must have the genotype RR. She can only pass on an R allele. Combined with Oscar’s RB, the possible offspring are 50% RR (red) and 50% RB (purple)—no blue-haired child possible.
Thus, to maximize the chance of having blue-haired offspring, Oscar should first seek a wife with blue hair, followed by one with purple hair.
