Question 394626
P(Z|def) = P(def AND Z)/P(def)

=(P(def|Z)*P(Z))/(P(def|X)*P(X) + P(def|Y)*P(Y) + P(def|Z)*P(Z))

= 0.06*0.40/(0.05*0.24+0.10*0.36+0.06*0.40) = 0.024/0.072 = 1/3