The proportion of the dominant allele of a certain gene in a

The proportion of the dominant allele of a certain gene in a population is 0.75. The recessive proportion is 0.25. A sample of 20 members of the population is taken and their genotypes determined. What is the probability that the sample had 12 pure dominant, 2 pure recessive, and 6 mixed genotypes?

Solution

Let the dominant allele be A. Proportion of dominant allele 0.75. Proportion of homozygous genotype= 0.75*0.75 = 0.562

Let the recessive allele be a.  Proportion of recessive allele 0.25. Proportion of homozygous genotype = 0.25*0.25 = 0.0625

Proportion of heterozygous: p² + 2pq + q² = 1

= (p + q)² =1

= 0.562+ 2pq+ 0.0625 = 1

= (0.75+0.25)² =1

2pq = 2*0.75*0.25 = 0.375

Therefore proportion of mixed genotype is 0.375.

The probability that 12 of 20 members are homozygous for A = 12*0.562 / 20 = 0.3372

The probability that 2 are pure recessive (aa)= 2*0.0625 / 20 = 0.00625

The probability that 6 are mixed genotype Aa = 6*0.375 / 20 = 0.1125