Phenotype frequencies ?

Question

3 allels at a locus, brown dominant to pink and yellow, pink dominant to yellow. what are the frequencies of the B P and Y alleles if the phenotypic frequencies are Brown 64, Pink 27, and Yellow 9?

a. 0.60, 0.15, 0.25
b. 0.60, 0.10, and 0.3
c. 0.35, 0.15, and 0.50
d. 0.4, 0.3, an 0.3
e. 0.64, 0.27, 0.09

The answer should be d but I dont understand why. Isn't phenotype the expression of gene? so why isn't the answer e if they tell us that there are 64 brown, 27 pink and 9 yellow??

Thanks for your help!

Answer 1

They give you the phenotypic frequencies. However, they want the allelic frequencies, which are how often the particular allele (B, P or Y) shows up in the gene pool.

The easy way to think about it is that the phenotype frequencies must add up to 1. Frequency is expressed as a portion of one, such as 0.25 or 0.7.
So, we can write the equation B + P + Y = 1
E is wrong immediately because these are phenotype frequences, not allelic frequencies.
The clue here is that yellow is the completely recessive allele; in order to be yellow, you need YY. Since 9 organisms out of 100 are yellow, that means 9% of the population has the genotype YY. Further, the probability (Pr) of being YY is the product of Pr (Y) and Pr(Y). Thus, 9% - or 0.09 - is the square of the Pr(Y). Pr(Y) is then sqrt(0.09) = 0.3.
Thus, our choices are not B or D, since only these two have the correct frequency for Y.
Next, think about pink. To be pink you can be PP or PY. Thus, the frequency of the P allele in the population must be higher than that of the Y allele. From the choices, this is true only in D. Therefore, D is correct.

Answer 2

Brown can be BB, BP, BY.
Pink can be PP, PY
Yellow must be YY.

Phenotype is determined by two alleles, not just one.