A question from MrSkeptiK: Genetics Word Problem?
What are the chances of the following couple producing a child with the autosomal genetic defect cystic fibrosis. Mark and his old wife, Janet, have a child with cystic fibrosis. His new wife, Ellen, had a brother with cystic fibrosis. Mark and Ellen, neither having cystic fibrosis, have a child. What is the chance that their child will have it?

I already asked it but due to varying results I figured another shot wouldn’t do any harm.

Selected answer:

Answer by Kristin
Cystic fibrosis is a recessive trait. I’ll represent the alleles with the letter C. The genotype CC would be two normal alleles, so no illness and no chance of passing it on. The genotype Cc would be one normal and one affected allele, so no illness, but a chance of passing it on. The genotype cc would be two affected alleles, so the person would have the illness.

Because Mark and Janet had a kid with CF, we know that Mark is a carrier (Cc).

Ellen’s brother had CF, which means that both of her parents were carriers (because there is no mention of her parents being affected themselves). Each time her parents reproduced, they had a 25% chance for CC, 50% chance for Cc, and 25% chance for cc. Because Ellen doesn’t have CF, we know that she is not cc. Thus, she has a 1/3 chance to be CC and a 2/3 chance to be Cc.

If Ellen is CC and reproduces with Mark who is Cc, there is a 0% chance that the child will have CF, so we don’t care about that.

If Ellen is Cc and reproduces with Mark, they have a 25% chance of having a kid with CF.

So we multiply Ellen’s chance of being Cc (2/3) by the chance of Mark and Ellen having a cc baby (25%) and we get 0.167, or 16.7%

Whether you agree or disagree, why not leave your own thoughts below.

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