Red-Haired Population Genetics Problem

What is the likelihood that a non-redheaded European is a carrier for the MC1Rr allele?

A: 22%

B: 33%

C: 11%

D: 44%

Answer:

The correct answer is 33%.

In Europe, approximately 4% of people are red-haired due to a recessive mutation in the melanocortin 1 receptor (MC1R). When the population is in Hardy-Weinberg equilibrium, the likelihood that a non-redheaded European is a carrier for the MC1Rr allele can be calculated as follows:

Let's denote the frequency of the recessive allele (q) as 0.2, as 4% corresponds to 0.04. According to Hardy-Weinberg equilibrium, the sum of the frequencies of the dominant allele (p) and the recessive allele (q) is 1. Therefore, p = 1 - q, p = 0.8.

The total population with non-red hair can be calculated using the Hardy-Weinberg equation: p^2 + 2pq. This gives us 0.64 + 0.32 = 0.96.

To find the percentage of the population that are non-redheaded carriers for the MC1Rr allele, we calculate 2pq/total population = 0.32/0.96 * 100 = 33%.

Therefore, the likelihood that a non-redheaded European is a carrier for the MC1Rr allele is 33%.