Give correct answer with detailed explanation....

1. Consider the full joint distribution (Figure 12.3): toothache -toothache catch -catch catch -catch cavity 0.108 0.012 0.072 0.008 -cavity 0.016 0.064 0.144 0.576 a). Find P(Toothache), P(Cavity) and P(Catch). b). Determine if toothache and catch are independent of each other. c). Find P ( toothache] Cavity). d). Find P(catch ] Cavity). e). Find P(toothache A catch] Cavity). f). Determine if toothache and catch are conditionally independent, given Cavity. g). Find P(Cavity | toothache A catch) using Bayes' rule and normalization