Exercise 14.2

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 $X_3$.

1. Draw the Bayesian network corresponding to this setup and define the necessary CPTs.

2. Calculate which coin was most likely to have been drawn from the bag if the observed flips come out heads twice and tails once.