Cystic Fibrosis - How can I find out the risk of Maria and James child getting it?

Question

So this is the deal: Maria has a child with cystic fibrosis. Now she has met a new guy, James, and plan to get a child with him. What is the risk of her second child getting it aswell?

Were they both come from, the general population CF occurance is 1 per 1600 inhabitants.

I know that to calculate the risk of James being a carrier I'd use HWE: p2 + 2pq + q2 = 1 formula straight ahead and get something like this:

q= √1/1600 = 1/40

Carriers of CF: 2pq

p + q = 1

p = 1 - 1/40 = 39/40

2pq = 2 x 1/40 x 39/40 = 78/1600 = 4.9%

But how do I work it if I want to get the risk for their child specifically, considering Maria obviously has it in her?

Answer 1

You need to apply Bayes Theorem because there is prior risk i.e Maria is confirmed a carrier. Give me a chance to look it up.

I couldn't find the answer exactly. James risk is 1/20 rather than 1/40 .... in the pseudoscience of genetics 39/40 is taken as 1 so 2pq is 2x1x1/40 = 1/20...don't ask me why ?

The real question is what is the chance the baby will be cf child?

Its some thing like this

                           is cf                               isn't cf

Prior                  1/1600                            1-1/1600 =1599/1600

Condition           1/4x1/20                            1

as mother

is carrier

Joint probability1/1600 x1/4 x1/20           1 approx

Posterior Prob (1/1600x1/4x1/20)            1-1/12801

                            ------------------------

                             1+(1/1600+1/4+1/20)

So, the childs risk of having CF is 1/12801 when you multiply out the figures above. I think you add this to his general risk 1/1600 to give his increased risk

The idea of bayes Theorem is it adds in the fact we know the mother is a carrier of CF gene to the probabilty in general a child has CF.

I'm not really sure I'm right because I did my Human genetics degree in TCD and the lecturers hadn't a clue. But I know the increase in risk is usually small even though the mother is a confirmed carrier:) Sorry