Albinism in humans is controlled by a recessive gene c From

Albinism in humans is controlled by a recessive gene (c). From marriages between two normally pigmented carriers (Cc). Assume that from such a marriage (Cc X Cc) four children will be produced.

a. what is the probability that all four will be normal?

b. That three will be normal and one albino?

c. Two normal and two albino?

d. One normal and three albino?

e. All four albino?

Solution

As albinism is recessive, to become albino, the albino gene from each pair is selected. Then, 1/2*1/2 = 1/4 is the probability of an albino, and 1-1/4 = 3/4 is the probability of being normal.

Then,

a) P(4 normal) = (3/4)^4 = 81/256

b) P(3 normal and 1 albino) = C(4,3)(3/4)^3(1/4)^1 = 4 * 27/64*1/4 = 27/64

c) P(2 normal and 2 albino = C(4, 2)(3/4)^2(1/4)^2 = 27/128

d) P(1 normal and 3 albino) = C(4,1)(3/4)(1/4)^3 = 3/64           

e  P(4 albino) =   (1/4)^4 = 1/256