Consider a two-variable causal network with Boolean variables A and B, where A is a parent of B, and the following conditional probabilities:

P

(a) = 0.2 P(b |

a) = 0.9 P(b | ¬a) = 0.3.

Consider the counterfactual: “B is observed to be true; what is the probability of B if A was false?”

Draw the belief network that can be used to answer this question. Give all

(conditional) probabilities. What needs to be conditioned on and what is queried to answer this counterfactual question? What is the resulting answer? (This can be done by hand or using any belief network implementation.)