Of 200 chips inspected, 30 had defect X and 20 had defect Y, and 8 of these had both X and Y. Which of the following is the number of chips with neither defect?

Answer: C. 158

By the inclusion-exclusion principle (number with X or Y = number with X + number with Y − number with both), 30 + 20 − 8 = 42 chips have X or Y. The chips with both are counted in both the 30 and the 20, so they are subtracted once. The number of chips with neither defect is 200 − 42 = 158.

• A. This is 200 − 30 − 20 − 8 = 142, which subtracts the 8 chips with both defects again instead of adding them back.
• B. This is 200 − (30 + 20) = 150, which leaves the 8 chips with both defects counted twice.
• C. Correct. 200 − (30 + 20 − 8) = 158.