The ambiguity is in the initial statement. "Given an offspring is affected" can
mean
1) We know that the i'th offspring is affected and the statuses of the other
m-1 are unknown
2) We know the status of all m offspring and exactly one is affected.
3) We know the status of all m offspring and x (>0) are affected.
Use the most specific condition that you can confirm.
James Cui wrote:
> I have a problem of calculating a conditional probability, and want to know
> what is the right formula.
>
> Suppose a family consists of two parents and m offsprings. Consider a
> disease that affects both genders equally. Given an offspring is affected,
> what is the probability that neither two parents nor other m-1 offsprings
> are affected. Am I right to use the following formula ?
>
> Pr(F1=0; F2=1) / Pr(F2>0)
>
> where F1 is the number of affections in parents, and F2 is the number of
> affections among offsprings.
>
> Thanks,
> James.
