16.1 Often it is possible to make interesting qualitative inferences about probabilities in a Bayesian network without knowing exact numerical values of probabilities in the network. Consider the network in Figure 16.3a. Let both a and c be very rare events, and let all the links in the network correspond to the causality between events. So p(b|a) >> p(ba). Also d is much more likely when b and/or c happen. Determine the relation ( , or =) between the following probabilities:

(a) p(a): p(a

c) (Which is larger, p

(a) or p(a | c))

(b) p(a): p(a |

d)

(c) p(a

d) p(a | cd)

(d) p(d bc) p(d | abc) :