Bayes' theorem for two random variables A and B is defined as follows: $P(A \mid B) = P(B \mid A) \times P(A) / P(B)$

Thus: $P(Y \mid Z) = P(Z \mid Y) \times P(Y) / P(Z) = 0.8 \times 0.6 / 0.5 = 0.96 = 96\%$.

(Book 2, Module 12.2, LO 12.g)