Question

Consider the case of a small assembly plant with 50 employees. Each worker is expected to complete work assignments on time and in such a way that the assembled product will pass a final inspection. On occasion, some of the workers fail to meet the performance standards by completing work late or assembling a defective product. 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. After reviewing the performance data, the production manager decided to assign a poor performance rating to any employee whose work was either late or defective. What is the probability that the production manager assigned an employee a poor performance rating? (Hint: Use the addition law.)

Answer 1

Total number of workers = 50

Number of workers completed work late = 5

Number of workers workers assembled a defective product = 6

Number of workers both completed work late and assembled a defective product = 2

Number of employee whose work was either late or defective = Number of workers completed work late + Number of workers workers assembled a defective product - Number of workers both completed work late and assembled a defective product

Number of employee whose work was either late or defective = 5 + 6 - 2 = 9

P[ Number of employee whose work was either late or defective ] = Number of employee whose work was either late or defective / Total number of workers

P[ Number of employee whose work was either late or defective ] = 9/50

P[ Number of employee whose work was either late or defective ] = 0.18