One of the types of mental retardation in humans can be caused by a recessive gene linked by the X chromosome.

One of the types of mental retardation in humans can be caused by a recessive gene linked by the X chromosome. Albinism (lack of pigmentation) is caused by a recessive autosomal gene. In the family, healthy parents had a son – an albino with mental retardation. Determine the genotypes of the parents. What is the probability of the birth of healthy children in this family?

Let’s designate the gene that causes the considered form of mental retardation as f, and the chromosome in which it is inherited as X f. Accordingly, the chromosome with the gene for normal mental development will be designated as X F.

Let’s designate the gene that causes the development of albinism in humans as k, then the gene that causes the development of normal pigmentation will be designated as K.

A son with albinism and mental retardation has the kkX f Y genotype.

For albinism, he is homozygous, because otherwise this trait could not be realized in the phenotype, because it is recessive. He inherits recessive genes from both healthy, according to the condition of the task, parents. Therefore, parents for albinism are heterozygous – Kk.

The Y chromosome, which determines male development, is inherited by the boy from his father. A chromosome with a pathological gene – X f – from a healthy mother, which allows us to conclude about the latent carriage of the pathological gene, about the heterozygosity of the mother’s genotype.

Thus, the father’s genotype is KkX F Y, he produces four types of spermatozoa – KXF, kX F, KY, kY. The mother has the genotype KkX F X f and produces four types of eggs – KX F, k X f, K X f, kX F.

healthy girls (KKX F XF, 2Kk XF X f, KK XF X f, 2KkX F XF);

girls with albinism (kk XF X f, kkX F XF);

healthy boys (KKX F Y, 2KkX F Y);

boys with mental retardation (2Kk X f Y, KK X f Y);

boys with albinism and mental retardation (kk X f Y);

boys with albinism (kkX F Y).

Healthy children – 9 out of 16 genotypes, or 56.25%.

Answer: the probability of having a healthy child for this married couple is 56.25%.