For the Bayesian Network shown below, without using any software tool, find

a) P(p1/x1), when x is instantiated (15 points)

b) P(q1/p1), when p is instantiated (15 points)

c) P(w1/p1), when p is instantiated (15 points)

Assume all nodes have binary states.

P(X1) = 0.2 P(Z1/X1) = 0.2 P(y1/X1) = 0.1 y P(Z1/X2) - 0.4 P(y1/X2) = 0.2 P(q1/Z1) = see instructions W b P(q1/Z2) = see P(w1/y1, Z1) = 0.2 instructions P(w1/y1, Z2) - 0.3 P(W1/y2, Z1) = 0.5 P(WI/y2, Z2) = 0.8 P(p1/W1, q1) = 0.3 p P(p1/WI, q2) = 0.1 P(p1/w2, q1) = 0.8 P(p1/W2, q2) - 0.3 Additional information: since neither y and z nor w and q are not root nodes and there is no information if they are independent; use P(y,z) = P(y)P(z/y), and P(w,q) = P(w)P(q/w). Do not