Computing Probabilities from ``Joint''

Compute the probability of any propositional sentence:

• enumerate satisfying assignments
• add their probabilities (disjoint)

$$\Pr(\mbox{\rm happy}+ (\mbox{\rm hungry}= \overline{\mbox{\rm happy}})) = 0.94.$$

Marginalize:

• $\Pr(\overline{\mbox{\rm hungry}}) = \Pr(TF)+\Pr(FF) = 0.45$

Conditional:

• $\Pr(\overline{\mbox{\rm happy}}\vert\mbox{\rm hungry}) = 0.54/0.55 = 0.98$