QUESTION 24 (10 points) - Probabilities of Binary Outcomes

A service process has three serial stages. The defect percentage at stage one is 9%. The defect percentage at stage two is 12%. And, the defect percentage at stage three is 6%. Use 5 decimal places for probabilities and 2 decimal places for sigma levels in the following situations.

(a)[2] Situation A: the connection logic of the three stages is that a good overall outcome only happens if all three stages individually have good outcomes. Draw the event tree for this situation. Calculate the probability of defective overall outcomes and the probability of good overall outcomes. Using Excel, calculate the corresponding sigma level and make a statement.

(b)[2] Situation B: the connection logic of the three stages is that a good overall outcome happens when at least one stage has good outcome. Draw the event tree for this situation. Calculate the probability of defective overall outcomes and the probability of good overall outcomes. Calculate the corresponding sigma level and make a statement.

(c)[3] Situation C: the connection logic of the three stages is that a good overall outcome happens when at least two stages individually have good outcomes. Draw the event tree for this situation. Calculate the probability of defective overall outcomes and the probability of good overall outcomes. Calculate the corresponding sigma level and make a statement.

(d)[3] Give some possible real-life processes for the three situations above.