Question

In a population of 100 cockroaches, a student discovers one individual who is bright blue. The student discovers that this individual is heterozygous for a dominant mutant allele and has one copy of it (cockroaches are diploid). A pleiotropic effect of the mutation is that it confers resistance to all insecticides. But no insecticides are being used in the student's apartment building and there are no other pleiotropic effects of this blue mutation. What is the probability that, by chance alone, this mutant allele will eventually be fixed in the population?

A) 1.00; it will certainly be fixed.

B) 0.00; it will certainly be lost.

C) 1/100 or 0.01

D) 1/200 or 0.005

E) There is insufficient information to answer correctly

Answer 1

The probability that the mutant allele will eventually be fixed in the population is 0.999.

Step-by-step explanation:

The probability that the mutant allele will eventually be fixed in the population can be calculated using the Hardy-Weinberg equation. The equation is p^2 + 2pq + q^2 = 1. In this case, the wild-type allele is represented by p and the mutant allele is represented by q.

Since the student discovered one individual who is heterozygous for the mutant allele, the frequency of the mutant allele (q) is 1/100, or 0.01. The frequency of the wild-type allele (p) can be determined by subtracting the frequency of the mutant allele from 1, which gives 0.99.

Using these values in the Hardy-Weinberg equation, we can calculate the probability of the mutant allele becoming fixed in the population: (0.99)^2 + 2(0.99)(0.01) + (0.01)^2 = 0.9801 + 0.0198 + 0.0001 = 0.999.