MEN 2A is a dominant inherited disease caused by a mutation in the RET proto-oncogene. The probability of being sick when you have the mutation of the RET proto-oncogene varies with age and is assumed to be 40% at 40 years of age.
With autosomal dominant inherited diseases, this formula can be used, where p indicated penetration and D is the sick allele:
P(II inherits D given that II is healthy) = $\frac{1-p}{2-p}$
The uncle of the son III1 in the tree has the disease so he assumes it comes from I1 or I2. The father of the son II2 is 40 years old with no symptoms.
What are the odds of the father having the mutation?
What are the odds of the son having the mutation knowing the % in the first question?
I just used the formula above as so for the first question: $$\frac{1-0.4}{2-0.4} = 37.5\%$$
I'm having problems with the second though and I assume to use Bayes formula.
I've tried as so:
$$P(\text{son mut given dad mut}) = \frac{P(\text{Dad mut given son mut}) \cdot P(\text{son mut)}}{P(\text{Dad mut})}$$
I know the probability of the dad having the mutation is 37,5% and the probability of the dad having the mutation given that his son has the mutation is 100%. However I can't seem to know what to put in the probability of the son having the mutation? Any help appreciated, thanks! Sorry for a long question.