Suppose we have a bag of three biased coins, , , and , with probabilities of coming up
heads of 25%, 50% and 70%, 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 ,
, and
Create a Bayesian network corresponding to this setup and define the necessary conditional probability tables.
Calculate which coin was most likely to have been drawn from the bag if the observed flips come out heads twice and tails once.