Exercise 17. A manufacturer examines its records over the last year on a component part received from outside suppliers. The breakdown on source (supplier A, supplier B) and quality (H: high, U:...

Exercise 17. A manufacturer examines its records over the last year on a component part received from outside suppliers. The breakdown on source (supplier A, supplier B) and quality (H: high, U: usable, D: defective) is shown in the two-way contingency table.
H U D
A 0.6937 0.0049 0.0014
B 0.2982 0.0009 0.0009
The record of a part is selected at random. Find the probability of each of the
following events.
a. The part was defective.
b. The part was either of high quality or was at least usable, in two ways: (i) by adding numbers in the table, and (ii) using the answer to (a) and the
Probability Rule for Complements.
c. The part was defective and came from supplier B.
d. The part was defective or came from supplier B, in two ways: by finding the cells in the table that correspond to this event and adding their probabilities, and (ii) using the Additive Rule of Probability.