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Neither Tim nor Rhoda had Duchenne muscular dystrophy, but their firstborn son does. What is the probability that a second child will have the disease? What is the probability if the second child is a boy? A girl?

Short Answer

Expert verified

The probability that the second child will have Duchenne muscular dystrophy is one-fourth (1/4) because they have a half-chance each of receiving Y chromosome from father and being a son and receives defective allele from mother.

The probability that the second child will be diseased if he is a boy is half (1/2) because they have a half-chance of receiving defective X-chromosome from mother.

The probability that the second child will be diseased if it is a girl is zero chance because they receive just either X chromosome.

Step by step solution

01

Duchenne muscular dystrophy

Duchenne muscular dystrophy is a recessive disorder. It is an X-linked disease that results in the degeneration of muscles.The condition occurs due to the defect caused by protein dystrophin.

Here, the parents are not diseased, but their first child is diseased. This means the parents must be carriers for the disease and transmit their defective alleles to the first child.

02

Probability for the second child with Duchenne muscular dystrophy

A son (XY) receives an X chromosome from his mother and a Y chromosome from his father. Girls (XX) receive one X chromosome from their mother and the other from their father.

The probability that the second child will also be diseased is 录. This is because the second child has 陆 chance that he receives the Y chromosome from the father or X-chromosome from the mother and 陆 chance that he will receive the defective X-chromosome from his mother.

Thus, the second child has a 录 (1/2 from Y chromosome x 陆 from defective X chromosome) chance of having Duchenne muscular dystrophy.

03

Probability for a second child to be diseased if it is a boy

Son receives an X chromosome from his mother, and Duchenne muscular dystrophy is an X-linked disease.The son receiving an X-chromosome will have 陆 chances of being diseased because it can either receive a diseased X-chromosome or a normal X-chromosome from his mother.

Thus, the probability for a second child to be diseased if it is a boy is 陆.

04

Explanation for probability for a second child to be diseased if it a girl

Girls possess two X-chromosomes, andDuchenne muscular dystrophy is an X-linked recessive disease.This means the presence of both diseased X-chromosomes is a must for the disease to occur in girls.

The presence of one diseased X-chromosome makes the girl a carrier for the disease. Thus, the probability for the second child to be diseased if it is a girl is zero. However, the girl has 陆 chance to be the carrier for the disease if she receives the diseases X-chromosome.

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