Manufacturing Bayes. A factory has three types of machines producing an item. The probabilities that the item is conforming if it is produced on the i th machine are given in the following table: The...

Manufacturing Bayes. A factory has three types of machines producing an item. The probabilities that the item is conforming if it is produced on the i_th
machine are given in the following table:

The total production is distributed among the machines as follows: 30% is done on type 1, 50% on type 2, and 20% on type 3 machines. One item is selected at random from the production.

(a) What is the probability that it is conforming?

(b) If it is conforming, what is the probability that it was produced on a type 1 machine?