9. At the end of a performance evaluation period, the production manager found that 5 of the 50 workers completed work late, 6 of the 50 workers assembled a defective product, and 2 of the 50 workers both completed work late and assembled a defective product. Required: A. What is the probability of late performers and defective product? B. What is the probability of late performers or defective product?

To find the probabilities, we’ll use the principles of set theory and probabilities. A. The probability of workers who completed work late and assembled a defective product can be calculated using the formula: P(A ∩ B) = Number of workers who are late and defective / Total number of workers = 2/50 = 0.04. So, the probability is 0.04 or 4%. B. For the probability of either late performers or defective product, we can use the formula: P(A ∪ B) = P(A) + P(B) - P(A ∩ B). First, calculate P(A) = (5 late workers / 50 total) = 0.1, and P(B) = (6 defective workers / 50 total) = 0.12. Now plug in the values: P(A ∪ B) = 0.1 + 0.12 - 0.04 = 0.18. Thus, the probability of late performers or defective products is 0.18 or 18%.