Suppose we have the Bayesian network in Figure 3, M = {H,C}, D = {B,L}, and m = {h1,c1}. Then a most probable explanation for m contains values of B and H that maximize P(B,L|h1,c1). The chain rule gives a straightforward algorithm for computing the most probable explanation. That is, if D={D1,D2,...,Dn}, M={M1,M2,...,Mn}, m={m1,m2,...,mn}, and d={d1,d2,...,dn} is a set of values of the variables in D, then P(d|m) = P(d1,d2,...,dn|m1,m2,...,mn) = P(d1|d2,...,dn,m1,m2,...,mn) * P(d2|d3,...,dn,m1,m2,...,mn) * ... * P(dn|m1,m2,...,mn). We can compute all the probabilities in the expression on the right using our algorithms for doing inference in Bayesian networks. So to determine a most probable explanation, we simply use this method to compute the conditional probabilities of all the explanations and take the maximum. Compute the most probable explanation for the instance before, P(B,L|h1,c1). P(h1) = 0.2, P(B|h1) = 0.25, P(B|h2) = 0.05, P(L|h1) = 0.003, P(L|h2) = 0.00005, P(F1|B1,L1) = 0.75, P(F1|B1,L2) = 0.10, P(F1|B2,L1) = 0.5, P(F1|B2,L2) = 0.05, P(C1|1) = 0.6, P(C1|1z) = 0.02.