ProbabilityMCQPYQ Jun 23Question 2841 of 295
All Questions On a commodity exchange when booking trades with provision for stop-losses, a trader can make a profit of or incur a loss of
Select Your Answer (Keyboard: A, B, C, D)
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Correct Answer
✅ Option a —
All Options:
- A
Rs 32 , 500 \displaystyle \text{Rs } 32,500 - B
Rs 35 , 000 \displaystyle \text{Rs } 35,000 - C
Rs 30 , 000 \displaystyle \text{Rs } 30,000 - D
Rs 40 , 000 \displaystyle \text{Rs } 40,000
Detailed Solution & Explanation
Due to a PDF parsing error, the profit amount in the question is incorrectly printed as Rs. 20,000 instead of Rs. 50,000.
Let's use the correct values to find the expected profit:
- Profit (X 1 \displaystyle X_1 ) = +Rs. 50,000 with probability P 1 = 0.75 \displaystyle P_1 = 0.75
- Loss (X 2 \displaystyle X_2 ) = -Rs. 20,000 with probability P 2 = 0.25 \displaystyle P_2 = 0.25
The expected profit E ( X ) \displaystyle E(X) is:
E ( X ) = X 1 P 1 + X 2 P 2 \displaystyle E(X) = X_1 P_1 + X_2 P_2
E ( X ) = ( 50 , 000 × 0.75 ) + ( − 20 , 000 × 0.25 ) \displaystyle E(X) = (50,000 × \displaystyle \times 0.75) + (-20,000 × \displaystyle \times 0.25)
E ( X ) = 37 , 500 − 5 , 000 = 32 , 500 \displaystyle E(X) = 37,500 - 5,000 = 32,500 .
So the expected profit is Rs. 32,500.
Hence, **Option A** is the correct answer.
About This Chapter: Probability
Paper
Paper 3: Quantitative Aptitude
Weightage
5-7 Marks
Key Topics
Probability Operations, Expected Value
A logic-heavy chapter dealing with random experiments, events (mutually exclusive, exhaustive), set theory probability, conditional probability, and Bayes' Theorem. It forms the basis for Theoretical Distributions.
View Official ICAI SyllabusExam Strategy Tip
Always draw a quick Venn Diagram or tree when faced with 'At least one' or 'Only A but not B' wording. It saves you from double-counting.
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