= Solution
Under the original assumptions the extra affected child is impossible. A generation-3 woman can have at most one copy of the unique introduced disease <allele>, while an unrelated outside spouse has none. Their children cannot inherit two defective copies. Thus both linkage and no-linkage <likelihoods> of the enlarged data are zero, and \b[the original single-entry model has no defined updated <LOD score>]. At least one assumption must be relaxed: another introduced disease <allele>, a new mutation, a phenocopy, or the relationship of the outside spouse.
If the model is enlarged to allow an independent outside <genetic carrier>, the reported extra information contains disease status but no new <genetic marker> <genotypes>. In the simple extension with fixed outside heterozygous-carrier <probability> $c$, the old disease observations force both generation-2 family ancestors to be <genetic carriers>. A further generation-3 sister inherits the disease copy with <probability> $1/2$, independently of the existing offspring transmissions. Given that she and her spouse are <genetic carriers>, exactly one of their three children is affected with <probability>
$$
\binom31\frac14\left(\frac34\right)^2=\frac{27}{64}.
$$
The additional <phenotype> <likelihood> is therefore $27c/128$. It is the same at $\theta=0$ and $\theta=1/2$, so it cancels and \b[the LOD remains unchanged in this phenotype-only, independent-carrier extension]. If the identity of the affected child is specified, the factor is $9c/128$, which also cancels. No such conclusion applies automatically if new <genetic marker> data are supplied or the revised <pedigree founder> model couples this branch to the old <genetic marker> evidence.
In general an enlarged data set changes the score by
$$
\Delta Z=\log_{10}\frac{P(\text{new data}\mid\text{old data},\theta=0)}{P(\text{new data}\mid\text{old data},\theta=1/2)},
$$
after choosing a coherent model with positive <likelihood>. The additional affected child alone does not justify assigning it the <autozygosity> evidence of an affected child of a cousin marriage.
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