A new production process at Fabufirst, Inc. has two in-line stages. The probability of defective components being produced in stage 1 is 15 percent and 10 percent in stage 2. Assembled units that have defective components only from stage 1 OR only from stage 2 are considered repairable. However, items that have defective components from both stage 1 and stage 2 (completely defective”) must be scrapped.

a.) Use a probability tree diagram and calculate the probabilities that the Fabufirst assembled units are:

(i) Defective in stage 1 and defective in stage 2 (are completely defective);

(ii) Defective in stage 1 and are not defective in stage 2 (called Repairable I);

(iii) Not defective in stage 1 but are defective in stage 2 (called Repairable II); and

(iv) Not defective in stage 1 and are not defective in stage 2 (completely good).

(v) What is the probability of producing repairable assembled units?

b.) Explain the results in terms of the multiplication and the addition rules for probability.