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.

Answer rating: 100% (QA)

a i The probability of producing completely defective assembled units is the probability of both stages 1 and 2 being defective which can be calculated using the multiplication rule The probability of stage 1 being defective is 015 and the probability of stage 2 being defective is 010 Therefore the probability of both stages being defective is 015 x 010 0015 ii The probability of producing Repairable I units defective in stage 1 but not in stage 2 is the probability of stage 1 being defective and stage 2 being not defective which can be calculated using the multiplication rule The probability of stage 1 being defective is 015 and the probability of stage 2 being not defective is 1 010 090 Therefore the probability of producing Repairable I units is 015 x 090 0135 iii The probability of producing Repairable II units not defective in stage 1 but defective in stage 2 is the probability of stage 1 being not defective and stage 2 being defective which can be calculated using the multiplication rule The probability of stage 1 being not defective is 1 015 085 and the probability of stage 2 being defective is 010 Therefore the probability of producing Repairable II units is 085 x 010 0085 iv The probability of producing completely good assembled units is the probability of both stages 1 and 2 being not defective which can be calculated using the multiplication rule The probability of stage 1 being not defective is 1 015 085 and the probability of stage 2 being not defective is 1 010 090 Therefore the probability of producing completely good assembled units is 085 x 090 0765 v The probability of producing repairable assembled units is the sum of the probabilities of producing Repairable I units and Repairable II units which can be calculated using the addition rule The probability of producing Repairable I units is 0135 and the probability of producing Repairable II units is 0085 Therefore the probability of producing repairable assembled units is 0135 0085 022 b The results of the probability tree diagram can be explained in terms of the multiplication and the addition rules for probability The multiplication rule was used to calculate ... View the full answer