Myotonic dystrophy is an autosomal recessive disorder affecting 1 in 500 people in Quebec

Answer:

(a) 0.9552

(b) 0.04472

(c) 99.99%

(d) 2.283 %

(e) 684820 people

Step-by-step explanation

Lets apply Hardy-Weinberg equations;

p2 + 2pq + q2 = 1

p + q = 1

Whereby;

p = frequency of the dominant allele

q = frequency of the recessive allele

p2 = % of homozygous dominant individual in the population

2pq = % of heterozygous individual in the population

q2 = % of homozygous recessive individual

(a)

% of homozygous recessive individual = 1/500 x 100 = 0.2 % or 0.002 hence;

q2 = 0.002

q = (0.002)^1/2 =0.04472

p + q = 1

p = 1 - q

p = 1 - 0.04472 =0.9552

The frequency of the homozygous dominant allele = 0.9552

(c)

frequency of homozygous recessive allele = q =0.04472

(d)

% of homozygous normal for the allele = p2

p =0.9552

p2 = (0.9552)^2 = 0.9999 or

p2 = 0.9999 x 100% = 99.99%

(d)

q2 = 1/7500 x 100 = 0.013333 % or 0.00013333

q = (q2)^1/2

q = (0.000133333)^1/2 = 0.011547

p + q = 1

p = 1 - q

p = 1 - 0.011547

p = 0.98845

% of heterozygous individuals/carriers = 2pq

2pq = 2(0.98845 x 0.011547) = 0.022827

2pq = 0.022827 x 100 % = 2.283 %

(e)

Number of expected to carriers = percentage of carriers/100 x 30 million

Number of expected to carriers = 2.283/100 x 30000000

Number of people expected to be carries = 684820 people