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Cystic fibrosis (CF) is a genetic disorder that affects mostly the lungs, but also the pancreas,...

Cystic fibrosis (CF) is a genetic disorder that affects mostly the lungs, but also the pancreas, liver, kidneys, and intestine. CF is inherited in an autosomal recessive manner with simple Mendelian inheritance. It is caused by the presence of mutations in the gene for the cystic fibrosis transmembrane conductance regulator (CFTR) protein.

A normal couple intends to have children but consult a genetic counselor because the man has a sister with CF and the woman has a brother with CF. There are no other known cases in their family. They want to know:

(1) What is the probability that their first child would be normal? (2) What is the probability that their first two children would have CF? (3) If they would like to have five children, what is the probability

that at least two of them would be normal?

Solutions

Expert Solution

From the given situation, it is clear that both the parents of couple are carriers of the recessive gene because it is the only possible case for a child to develop the disease. And here, man's sister is affected and woman's brother is affected.

There are three possible situations for the genotype of the couple, both can be normal or both can be carriers or either of them can be carrier.

1). Situation A

if both individuals are carriers then, AACF AACF, there is 75% chances are of getting a normal child.(25% of getting AA, 50% of getting AACF and 25% of getting ACFACF) and we know that the recessive gene will only get expressed in homozygous condition.

Hence, the probability of getting a normal child will be 0.75

Situation B

if either of the parent is a carrier then, AACF AA, there is 100% chance of getting a normal child (50% of AA, 50% of AACF) no homozygous condition to express the gene.

here the probability will be 1.

2). from above explanation in situation A, only 25% chances are of getting a diseased child.

So, the probabilty of getting first two children havin CF will be 1/2.(according to sum rule of probability)

situation B will only produce normal children.

3). If the couple decides to have 5 children and chances of getting a normal child is 75% (we will only consider situation A because situation b will give rise to normal offspring only)

So the probability of getting atleast 2 normal children will be 100%.

gladiator answered 2 years ago
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