Question 3 (8 points). John has three biased dices in his bag, namely dice a, dice...

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Question 3 (8 points). John has three biased dices in his bag, namely dice a, dice b, and dice c. The probabilities of rolling an even number for these dice are 55%, 90%, and 80% respectively. He randomly chooses one of the dice (the choice is made with equal likelihood), and rolls the chosen dice four times to generate outcomes X, where i = 1, 2, 3, 4. (a) Draw the Bayesian Network corresponding to this setup and define its Conditional Probability Tables (CPTs). (3 points) (b) Calculate which dice was most likely to have been drawn from the bag if the observed rolls had one odd outcome and three even outcomes (the order of these outcomes is not known, meaning it could be {odd, even,even, even} or {even, odd, even, even} or {even, even, odd, even} and so on.). (5 points) Question 3 (8 points). John has three biased dices in his bag, namely dice a, dice b, and dice c. The probabilities of rolling an even number for these dice are 55%, 90%, and 80% respectively. He randomly chooses one of the dice (the choice is made with equal likelihood), and rolls the chosen dice four times to generate outcomes X, where i = 1, 2, 3, 4. (a) Draw the Bayesian Network corresponding to this setup and define its Conditional Probability Tables (CPTs). (3 points) (b) Calculate which dice was most likely to have been drawn from the bag if the observed rolls had one odd outcome and three even outcomes (the order of these outcomes is not known, meaning it could be {odd, even,even, even} or {even, odd, even, even} or {even, even, odd, even} and so on.). (5 points)