Genetics question (firecracker question of the day spoiler)

[zhopv10]

Stem: "A husband and wife come to your clinic for preconception counseling. They are very concerned because the husband has two siblings with cystic fibrosis (CF); one who is awaiting a lung transplant and another who passed away at age 17. His wife does not have any family members with CF. The carrier rate for CF in the general population is approximately 1/25."

then it gives a bunch of options. the answer they give is 1/150

So clearly CF is autosomal recessive, and his siblings have been autosomal recessive so the parents needed to be heterozygous carriers (since it wasn't mentioned that either of them had the disease, and they have kids that have the disease). His options are basically 1/4 chance of being homozygous non carrier of the disease 1/2 chance being a carrier and 1/4 chance having the disease right? So we know he doesn't have the disease. So he is either a homozygous non carrier or a heterozygous carrier and for him to have a kid with CF he would need to be a heterozygous carrier of the gene so the 1/2 is what we would use right? Now the wife has a 1/25 chance of being a carrier so that is factored in too. So basically you would multiply the chance of him being a carrier by the chance of her being a carrier by the chance of if they are both carriers what the chance of them having a kid with CF is. So I would do 1/2 * 1/25 * 1/4= 1/200

So now the firecracker explanation was you would multiple 2/3 (his chance of being a carrier) by the 1/25 (the moms chance of being a carrier) by 1/4 (the chance that if they were both carriers they would have a son with cystic fibrosis) giving 1/150.

Now I follow everything except that 2/3... I would think it would be 1/2 since that is his chance of being a carrier?? I'm terrible with genetics so i'm sure i'm missing something but does anyone know why it would be 2/3 for his chance of being a carrier and not 1/2?

Thanks!

---

Members don't see this ad.

 

[zhopv10]

Ah, actually I just figured it out/noticed it in the explanation when I went through it again. I'll leave it up in case anyone else missed it/is interested. So the reason is we clearly know the husband does not have the disease, so we effectively remove the chance of him being a homozygous carrier of the CF gene and thus all that remains is the chance that he is a homozygous non carrier (1/3) or a heterozygous carrier (2/3 chance).

 

[dempty]

Ah, actually I just figured it out/noticed it in the explanation when I went through it again. I'll leave it up in case anyone else missed it/is interested. So the reason is we clearly know the husband does not have the disease, so we effectively remove the chance of him being a homozygous carrier of the CF gene and thus all that remains is the chance that he is a homozygous non carrier (1/3) or a heterozygous carrier (2/3 chance).

You nailed it. Remember, when you're dealing with conditional probabilities you take into account some other information. Like you said, he doesn't have the disease, so we know he can't be homozygous for the defective allele. You can also draw your punnet square and say "given that the husband doesn't have the disease, what are the chances he carries the allele?" Cross out the diseased box and you're left with 3 options, 2 of which are carriers.