We have a bag of three biased coins $a$, $b$, and $c$ with probabilities of coming up heads of 30%, 60%, and 75%, respectively. One coin is drawn randomly from the bag (with equal likelihood of drawing each of the three coins), and then the coin is flipped three times to generate the outcomes $X_1$, $X_2$, and $X_3$.
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Draw the Bayesian network corresponding to this setup and define the necessary CPTs.
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Calculate which coin was most likely to have been drawn from the bag if the observed flips come out heads twice and tails once.
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