Four Problems Bayes' Theorem tells us that, where: Ty P = p = Prob (A \\ B), ay + (1 - x)z x = Prob (A), y = Prob (B | A), z = Prob (B | not A). Problem #1 In our original version of the Genetic Disorder Problem, we have a prior of = 101, i.e., only 1 out of 101 children has the bad gene. We know that a test to detect the presence of this bad gene is 90% sensitive and 95% specific. (a) Explain why y = 0.90 and z = 0.05. (b) Calculate p, the probability that a child has the bad gene given that this child tested positive for this bad gene