A baker makes 3 special cakes every morning at a cost of Rs. 100 each and sells them at Rs. 250 each. A cake not sold on the same day is thrown away. The daily demand D for these cakes has the following probability distribution, where “3” stands for 3 or more cakes:
| D | 0 | 1 | 2 | 3 |
| P(D) | 0.1 | 0.2 | 0.3 | 0.4 |
The expected daily profit of the baker from these cakes is
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → Rs. 200
The baker can sell at most the 3 cakes made, and a demand of 3 or more means all 3 are sold. So the number of cakes sold has the distribution of D in the table. The cost of Rs. 300 is paid every day.
The expected number of cakes sold is
\(E(D) = 0 \times 0.1 + 1 \times 0.2 + 2 \times 0.3 + 3 \times 0.4\)
\(= 0.2 + 0.6 + 1.2 = 2\)
The profit is 250D − 300, so the expected profit is
\(E(250D - 300) = 250 \times 2 - 300\)
\(= 500 - 300 = 200\)
Why the other options are incorrect
Option (1) Rs. 500 — Incorrect. This is the expected sales income; the cost of Rs. 300 has not been subtracted.
Option (2) Rs. 450 — Incorrect. This is the profit only when all 3 cakes are sold, \(3 \times 150\).
Option (3) Rs. 100 — Incorrect. The expected profit is \(500 - 300 = 200\), not 100.