CMA Foundation · Fundamentals of Business Mathematics and Statistics · Probability
A trader in Surat estimates the daily profit from selling sarees as Rs 2,000 with probability 0.3, Rs 5,000 with probability 0.5 and Rs 8,000 with probability 0.2. What is the expected daily profit?
The expected daily profit is Rs 4,700. Mathematical expectation is the sum of each profit multiplied by its probability: 600 plus 2,500 plus 1,600 equals 4,700. Simply taking the middle value or adding the profits without weighting by probabilities gives wrong results.
- ARs 4,700Correct
- BRs 5,000
- CRs 4,500
- DRs 15,000
Explanation
E(X) = 2,000(0.3) + 5,000(0.5) + 8,000(0.2) = 600 + 2,500 + 1,600 = 4,700. Rs 5,000 is just the middle value, and Rs 15,000 is the plain sum of the outcomes with probabilities ignored.
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