\ dfrac {P (H|S)} {P (H^c|s)} =\ dfrac {P (H) P (S|H) P (E|S) + P (H) P (S^C|H) P (E|s^C)} {P (H^C) P (S|H^C) P (E|S) + P (H^C) P (S^C|H^C) P (E|s^C)}\) \(\dfrac{P(H|E^c)}{P(H^c|E^c)} = \dfrac{P(S) P(...\ dfrac {P (H|S)} {P (H^c|s)} =\ dfrac {P (H) P (S|H) P (E|S) + P (H) P (S^C|H) P (E|s^C)} {P (H^C) P (S|H^C) P (E|S) + P (H^C) P (S^C|H^C) P (E|s^C)}\) P(H|Ec)P(Hc|Ec)=P(S)P(H|S)P(Ec|S)+P(Sc)P(H|Sc)P(Ec|Sc)P(S)P(Hc|S)P(Ec|s)+P(Sc)P(Hc|Sc)P(Ec|Sc)