A company buys components from three suppliers. They get 50% from supplier 1, 20% from supplier 2 and the rest from supplier 3. Suppose that 2% of the components from supplier 1 are out of spec (denoted by "OOS"), 8% from supplier 2 are OOS and that 4% of components from supplier 3 are OOS. A component is selected at random. [Hint: It may be helpful to represent this information in a tree diagram.]
a. What is the probability that the part is from supplier 3?
b. What is the probability the part is not OOS if it is from supplier 1?
c. What is the probability the component is from supplier 1 and is OOS?
d. What is the probability the component is OOS?
e. What is the probability that the component is from supplier 1 if it is known to be OOS.