A chip costs ¥300 to make. A good chip sells for ¥500, and a defective chip cannot be sold and is discarded. If the probability that a chip is good is 80%, which of the following is the expected profit per chip made?

Answer: A. ¥100

The expected revenue is 500 × 0.8 + 0 × 0.2 = ¥400, and the manufacturing cost of ¥300 is incurred for both good and defective chips, so the expected profit is 400 − 300 = ¥100. Taking +¥200 for a good chip and −¥300 for a defective chip gives the same result: 200 × 0.8 + (−300) × 0.2 = 160 − 60 = ¥100.

• A. Correct. 0.8 × 500 − 300 = ¥100.
• B. This is 0.8 × (500 − 300) = 160, which leaves out the ¥300 spent on making the defective chips.
• C. 500 − 300 = 200 is the profit on one good chip and ignores the 20% of defective chips.