This question's explanation and your answers so far.
ある市場が今後, 拡大, 現状維持, 縮小する場合の商品 A, B, C の販売利益が表のとおり見込まれており, 拡大, 現状維持, 縮小する確率がそれぞれ 0.2, 0.5, 0.3 であるとき, どの商品を販売すると予想利益が最高となるか。ここで, 商品の予想利益は販売利益の期待値から開発コストを差し引いたものとし, 各商品 A, B, C の開発コストは, それぞれ 20 億円, 10 億円, 15 億円とする。 単位 億円
| 商品 | 拡大 | 現状維持 | 縮小 |
|---|---|---|---|
| A | 60 | 50 | 40 |
| B | 80 | 40 | 20 |
| C | 100 | 40 | 0 |
A has the largest expected value of the three products at 49 hundred million yen, but its development cost of 20 hundred million yen is also the highest, so after subtracting it the expected profit is only 29 hundred million yen. That falls short of B's 32 hundred million yen, so this is wrong. Looking only at the expected value and forgetting to subtract the development cost is the typical mistake that leads to choosing A.
正解 Expected profit = (expected value of the sales profit) − (development cost). An expected value is obtained by multiplying the profit in each scenario by the probability of that scenario and adding the results. First, the expected value of the sales profit: A is 60×0.2+50×0.5+40×0.3 = 12+25+12 = 49 hundred million yen, B is 80×0.2+40×0.5+20×0.3 = 16+20+6 = 42 hundred million yen, and C is 100×0.2+40×0.5+0×0.3 = 20+20+0 = 40 hundred million yen. Subtracting each product's development cost (A = 20, B = 10, C = 15 hundred million yen) gives expected profits of A = 49−20 = 29 hundred million yen, B = 42−10 = 32 hundred million yen, and C = 40−15 = 25 hundred million yen. The largest is B with 32 hundred million yen, so selling product B is the best choice. Therefore “イ” is the correct answer.
C looks attractive because its profit of 100 hundred million yen when the market expands is the largest, but the probability of expansion is only 0.2, and the profit when the market shrinks (probability 0.3) is 0 hundred million yen. Its expected value is only 40 hundred million yen, and after subtracting the development cost of 15 hundred million yen the expected profit is 25 hundred million yen, the lowest of the three products, so this is wrong. The key point is to judge by the probability-weighted expected value rather than by the maximum value.
When actually calculated, the expected profits are A = 29 hundred million yen, B = 32 hundred million yen, and C = 25 hundred million yen, all different values. They cannot all be the same, so this is wrong.