One of two biased coins A and B is selected and flipped 3 times. Let A be the event that coin A is selected and B be the event that coin B is selected, with probabilities p(A) = 0.1 and p(B) = 0.9.
When coin A is flipped, the probability of heads is 0.6.
When coin B is flipped, the probability of heads is 0.2.
Let HHH be the event that the selected coin comes up heads 3 times. Complete the values X, Y, and Z in Bayes' Theorem to determine the probability coin B was chosen if all 3 flips come up heads.
p(B|HHH) = (X * 0.9) / (Y * 0.9 + Z * 0.1)