# How many birds in this population would be expected to have either red or white feathers?

Question: The red and white feather pattern of a bird is determined by a gene that has two alleles, band R and W,which show codominance. Some birds have completely red feathers (RR),some parrots have completely white feathers (WW), and others have red and white feathers (RW).In a population of 630 birds that is at Hardy-Weinberg equilibrium, 202 parrots have completely red feathers. How many birds in this population would be expected to have either red or white feathers?

Is this question asking for what is the carrier proportion-2pq? The answer is supposed to be 321 but I keep getting 309. I did 202/630= p^2=0.32= 0.566. Then q=1-0.566 =0.434. Then I did 2(0.434)(0.5662)= 0.49. Then I multiplied 0.49 x 630 to get 309. If any one can point out what I did wrong I would really appreciate it!!

• If this is homework, please add the homework tag. – RHA Oct 16 '18 at 6:41
• Its nice to see someone actually do something before to post it on SE. :) – L.Diago Oct 16 '18 at 8:51

$$p^2 = 202 / 630 ≈ 0.32$$ $$p = \sqrt{202/630}$$ $$(1-p) = 1 - \sqrt{202/630}$$ $$(1-p)^2 = \left(1 - \sqrt{202/630}\right)^2 ≈ 0.188$$
There is a fraction of $$202 / 630 ≈ 0.32$$ of red birds. There is a fraction of $$\left(1 - \sqrt{202/630}\right)^2 ≈ 0.188$$ of white birds. There is therefore a fraction of $$0.32 + 0.188 = 0.508$$ of birds that are either all white or all red. In a population of 630 individuals, it therefore represents $$630 * 0.508 ≈ 320.53$$. A result that is apparently rounded up at $$321$$ in your answer key.
You computed the number of birds that have both white and red feathers (WR) while the question was asking for either red or white feathers. You calculated the expected number of heterozygotes instead of calculating the expected number of homozygotes.
Of course the number of heterozygotes and the number of homozygotes should add up to the number of individuals in the population ($$321 + 309 = 630$$).