Then the probability of obtaining N given the two groups is: P(N(S,L,K)|cij,πij,i,j∈x,y)=∏i∈(X,Y)∏j∈(X,Y)cijLijπijKij(1-cij)Zij(1-πij)Lij-Kij(2) Analagous to Eq 1, this likelihood is maximized when c^ij=LijLij+Zij and π^ij=KijLij for all combinations of groups.