### Hardy-Weinberg practice

Hardy-Weinberg tutorial (allele frequencies):

If 98 out of 200 individuals in a population express the recessive phenotype, what percent of the population are homozygous dominant?
49%
70%
30%
42%
9% X
**Solution**:
- Recessive phenotype implies homozygous genotype.
*q*^{2} = 98 / 200 = 0.49
*q* = 0.7
*p* + *q* = 1
*p* + 0.7 = 1
*p* = 0.3
*p*^{2} = *0.3*^{2} = 0.09

If 98 out of 200 individuals in a population express the recessive phenotype, what percent of the population are heterozygotes?
49%
70%
30%
42% X
9%
**Solution**:
- Recessive phenotype implies homozygous genotype.
*q*^{2} = 98 / 200 = 0.49
*q* = 0.7
*p* + *q* = 1
*p* + 0.7 = 1
*p* = 0.3
- 2
*pq* = 2 (0.7 * 0.3) = 0.42
- double check:
*p*^{2} + 2*pq* + *q*^{2} = 1?
- double check: 0.09 + 0.42 + 0.49 = 1.

**Brown hair (B) is dominant to blond hair (b). If there are 168 brown hairs in a population of 200:**

What is the predicted frequency of heterozygotes?
16%
40%
60%
48% X
84%
**Solution**:
- BB + Bb = 168 / 200 = 0.84 = brown hairs
- bb = 1 - 0.84 = 0.16 =
*q*^{2} blond hairs
*q* = 0.4
*p* = 1 - *q* = 1 - 0.4 = 0.6
- 2
*pq* = 2 (0.4 * 0.6) = 0.48

What is the predicted frequency of homozygous dominant?
16%
40%
60%
48%
36% X
**Solution**:

What is the predicted frequency of homozygous recessive?
16% X
40%
60%
48%
36%
**Solution**:
*q*^{2} = 0.4^{2} = 0.16

- double check:
*p*^{2} + 2*pq* + *q*^{2} = 1?
- double check: 0.6
^{2}< + 2 (0.6 * 0.4) + 0.4^{2} = 0.36 + 0.48 + 0.16 = 1.

**If blonds occur in 36% of the population:**

What is the allele frequency for b?
36%
60% X
40%
16%
48%
**Solution**:
- bb =
*q*^{2} = 0.36
*q* = b = 0.6

What is the allele frequency for B?
36%
60%
40% X
16%
48%
**Solution**:
*p* + *q* = 1
*p* + 0.6 = 1
*q* = 1 - 0.6 = 0.4

What is the predicted frequency of heterozygotes?
36%
60%
40%
16%
48% X
**Solution**:
- 2
*pq* = 2 (0.6 * 0.4) = 0.48

What is the predicted frequency of homozygous dominant?
36%
60%
40%
16% X
48%
**Solution**:
*p*^{2} + 2*pq* + *q*^{2} = 1
*p*^{2} + 0.48 + 0.36 = 1
*p*^{2} = 1 - (0.48 + 0.36)
*p*^{2} = 1 - 0.84
*p*^{2} = 0.16