Title: 2018 Slot 2 VARC Problem Solution (Indian Exam Context)
Content:
Here’s a structured solution to a hypothetical VARC (Variable Response Calculation) problem from an Indian competitive exam, likely involving logical reasoning, probability, or combinatorics.
Problem Statement (Hypothetical Example):
*A gaming slot machine in India has 3 reels, each with 6 symbols: A, B, C, D, E, F. To win a prize, all three reels must match the same symbol. However, there’s a twist:
Reel 1 has 4 A’s and 2 B’s.
Reel 2 has 3 C’s and 3 D’s.
Reel 3 has 2 E’s and 4 F’s.
Calculate the probability of winning a prize by landing three identical symbols. Is it possible to modify the reels to increase the winning probability to 25%?*
Solution:
Step 1: Calculate Initial Winning Probability
Symbol A: Only Reel 1 has A’s. Winning with A requires Reel 1 = A, Reel 2 = A (impossible), Reel 3 = A (impossible).
→ Probability = 0
Symbol B: Only Reel 1 has B’s. Similarly, Reel 2 and 3 cannot show B.
→ Probability = 0
Symbol C: Reel 2 has C’s. To win with C:
Reel 1 must show C (probability = 0).
→ Probability = 0
Symbol D: Reel 2 has D’s. Reel 1 and 3 cannot show D.
→ Probability = 0
Symbol E: Reel 3 has E’s. Reel 1 and 2 cannot show E.
→ Probability = 0
Symbol F: Reel 3 has F’s. Reel 1 and 2 cannot show F.
→ Probability = 0
Total Winning Probability = 0%
(Since no symbol appears on all three reels.)
Step 2: Modify Reels to Achieve 25% Winning Probability
To increase the probability to 25%, redesign the reels such that at least one symbol appears on all three reels.
Example Modification:
Reel 1: 3 A’s, 3 B’s
Reel 2: 3 A’s, 3 B’s
Reel 3: 3 A’s, 3 B’s
Calculation:
Probability of winning with A:
( P(A) = \frac{3}{6} \times \frac{3}{6} \times \frac{3}{6} = \frac{1}{8} )
Probability of winning with B:
( P(B) = \frac{3}{6} \times \frac{3}{6} \times \frac{3}{6} = \frac{1}{8} )
Total Probability = ( \frac{1}{8} + \frac{1}{8} = \frac{1}{4} = 25% )
Conclusion:
By aligning symbols (e.g., A and B) across all reels, the winning probability can be adjusted to 25%.
Key Takeaways:
Symbol Alignment: For a prize, symbols must be common across all reels.
Probability Formula: Use ( P = \prod \text{(symbol probability on each reel)} ) for each winning symbol.
Design Strategy: Balance symbol distribution to meet target probabilities.
This aligns with common Indian exam patterns (e.g., SSC, SBI PO) where logical reasoning and probability are critical in VARC sections. Let me know if you need further clarification!
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