One of two biased coins A and B is selected and flipped 2 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 0.4. When coin B is flipped, the probability of heads is 0.8.
Let HH be the event that the selected coin comes up heads 2 times. Complete the values X, Y, and Z in Bayes' Theorem to determine the probability coin B was chosen if both come up heads.
P(B|HH)