Sometimes a paternity test is needed based on a mixture of mother and child. That is, the embryo died or was aborted, and the only DNA available is the mother's type, the alleged father's, and a type from the abortus that is a combination of the mother and the embroyo.
In such a situation it's easy enough to work out the proper likelihood ratios from first principles. Before doing that ...
Mother  PR  
Mixture  PQR  
Alleged father  QS 
Definitions of probability symbols: 

The paternity index PI=X/Y where
X = Pr(such types  paternity by Alleged father), and Y = Pr(such types  man unrelated). Define M=Pr(mother's type)

X = M×F×Pr(Mixture  parents as alleged) = M×F×1/2;
Y = M×F×Pr(Mixture  Mother & random sperm) =
M×F×Pr(Q).
PI = ^{1} /
_{2Pr(Q)}
Note that this is the same formula as that for the normal paternity pattern
Mother  PR  
Child  PQ  
Alleged father  QS 
If the placental genetic data suggests more than one embroyo, a possible explanation is nonidentical twins from a single father. Computing likelihoods isn’t much harder than in the oneembryo problem.
Mother  PR  
Mixture  PQRS  
Alleged father  QS  
Define the probabilities X, Y, M, F as above. 
X = M×F×Pr(Mixture  parents as alleged) = M×F×1/2
— same formula though this time 1/2 is Pr(F contributes different
alleles to each embryo).
Y = M×F×Pr(Mixture  Mother & random pair of sperm) =
M×F×Pr(QS) =
M×F×2Pr(Q)Pr(S).
PI = ^{1} /
_{4Pr(Q)Pr(S)}