Solution (source code)

= Solution

Let $D$ denote the specified disease pattern. With one introduced disease-allele copy, no new mutations or phenocopies, and fully penetrant <recessive inheritance>, every affected subject must carry two descendants of that one copy. Since every sibship has an affected child, all the upstream <genetic carrier> transmissions described above are forced. Conversely, unaffected siblings cannot carry two disease copies. Thus $D$ implies the inheritance event $E$ at the causal <genetic locus>, and
$$
\boxed{P(E\mid D)=1.}
$$
The rarity of the unconditional pattern in part (d) does not make its <posterior probability> small after observing the pattern that forces it. If the location of the one disease copy is initially uniform among the four founding copies, the <likelihood> of $D$ is the same for each, so its posterior location remains uniform; $P(E_q\mid D)=1/4$ for any named copy. If $q$ is already designated as the disease copy, its corresponding event has <posterior probability> 1.