Question

A certain island-nation with a population of 200,000 has laws which severely restrict travel onto or off the island. There is an absolute prohibition against marrying foreigners, but island natives may marry as they wish. A non-lethal recessive genetic condition affects 2,000 of the people. How many carriers of this condition live on the island?

a. 198,000
b. 96,000
c. 36,000
d. 12,400
e. 9,600

Answer 1

To determine the number of carriers of the recessive genetic condition on the island, we need to first understand the inheritance pattern of the condition. Since the condition is recessive, individuals need to inherit two copies of the recessive allele to show the condition. Using the equations
`q^2`2,000/200,000 and 2pq, we can calculate the frequency of the recessive allele and the number of carriers on the island.

Step-by-step explanation:

To determine the number of carriers of the recessive genetic condition on the island, we need to first understand the inheritance pattern of the condition. Since the condition is recessive, individuals need to inherit two copies of the recessive allele to show the condition. Let's represent the dominant allele as A and the recessive allele as a.

Given that 2,000 individuals have the condition, they must all be homozygous recessive (aa). The frequency of the recessive allele can be calculated using the equation
`q^2`2,000/200,000, where q represents the frequency of the recessive allele. Solving for q, we find q = sqrt(2,000/200,000) = 0.1.

Since the condition is recessive, individuals who are carriers have the heterozygous genotype (Aa). The frequency of carriers can be calculated using the equation 2pq, where p represents the frequency of the dominant allele. Since p + q = 1, we can solve for p by subtracting q from 1. Therefore, p = 1 - 0.1 = 0.9. Finally, multiplying p by q by the total population (200,000) gives us the number of carriers, which is 0.9 * 0.1 * 200,000 = 18,000.