Question 8: (Bayes Theorem) John, Adam, and Elizabeth are baking cookies to raise money. John made 100 cookies, Adam made 60 cookies, and Elizabeth made 140 cookies. Only cookies with good conditions can be sold, so each cookie is checked for shape. (a) The number of defective cookies each person made are as follows: John: 20 cookies, Adam: 6 cookies, and Elizabeth: 21 cookies. If a randomly selected cookie is defective, what is the probability it was made by John? (b) Instead of the actual number of defective cookies (D), the defective rates for each person is given as the following: John: P(D|John) = 20% Adam: P(DIAdam) = 15% Elizabeth: P(DIElizabeth) = 10% If a randomly selected cookie is defective, what is the probability it was made by John