In humans eye color is complex but sometimes boils down to a

In humans, eye color is complex but sometimes boils down to a simple dominant to recessive relationship among alleles. So consider the brown eye color allele \'B\' which deposits melanin in the iris of the eye to yield brown pigmented eyes Interestingly, it is related to the gene that deposits melanin in the skin; more on that later. The allele \'b\' is a recessive mutant allele where the pathway to melanin deposition in the iris is disrupted (the \'B\' protein is either not produced at all, or the protein that is coded for has an active site that can\'t function) so that \'bb\' individuals have eyes that lack melanin and appear blue. If heterozygous children produce children, what are the following probabilities? The first two children will have blue eyes? That among a total of four children, 2 will have blue eyes, and 2 will have brown eyes? The first child will have blue eyes, but then the next three will have brown eyes?

Solution

If B denotes brown colour of the iris of eye and it is dominant gene and b is the recessive allele which gives blue appearance to the iris of eye when present in homozygous condition, the heterozygote individuals will be denoted as Bb.

Thus the cross would be Bb©Bb

Thus everytime a child is born, there is a 75% probability of having brown eyes and 25% probability of having blue eyes.

a. Probability of having the first two children with blue eyes is (1/4)×(1/4)=1/16.

b. In order to find the probability of having two children with blue eyes and two with brown eyes we need to use the gormula, ( nCk)p^k(1-p)^n-k where k number of children out of total n children have eyes of a particular colour which appears with probability p.

Thus, out of 4, probability of having two children with blue eyes and two with brown eyes are

(4C2)(1/4)^2(1-1/4)^4-2=0.42 or 42%

c. Probability of having first child eith blue eyes is 1/4 and next three children brown eyes is (3/4)^3. Thus total probability is (1/4)×(3/4)^3= 0.105=10.5%

Gametes	B	b
B	BB brown	Bb brown
b	Bb brown	bb blue