One of two biased coins \(A\) and \(B\) is selected and flipped. Let \(A\) be the event that coin \(A\) is selected and \(B\) be the event that coin \(B\) is selected, with probabilities \(p(A) = 0.3\) and \(p(B) = 0.7\). When coin \(A\) is flipped, the probability of heads is \(0.2\). When coin \(B\) is flipped, the probability of heads is \(0.8\).
Let \(H\) be the event that the selected coin comes up heads. Complete the values \(X\), \(Y\), and \(Z\) in Bayes' theorem to determine the probability coin \(B\) was chosen if the flip came up heads.