Title: 2022 Quant Slot 1 - Solution for Indian Game Problem
Problem Statement (Hypothetical Example):
In a traditional Indian game, players roll two six-sided dice. If the sum is 7, the player wins a prize of ₹100. If the sum is 5, they lose ₹50. For any other sum, the game continues. What is the expected value of a player’s profit after one round?
Solution:
Identify Possible Outcomes:
Each die has 6 faces. Total outcomes = (6 \times 6 = 36).
Sum = 7: Possible combinations: (1,6), (2,5), (3,4), (4,3), (5,2), (6,1) → 6 outcomes.
Sum = 5: Possible combinations: (1,4), (2,3), (3,2), (4,1) → 4 outcomes.
Other sums: (36 - 6 - 4 = 26) outcomes.
Calculate Probabilities:
(P(\text{Win}) = \frac{6}{36} = \frac{1}{6}).
(P(\text{Lose}) = \frac{4}{36} = \frac{1}{9}).
(P(\text{Continue}) = \frac{26}{36} = \frac{13}{18}).
Expected Value (EV) Calculation:
If the player wins: (+\ ₹100).
If the player loses: (- ₹50).
If the game continues, the expected value resets (no profit/loss in this round).
[
\text{EV} = \left(\frac{1}{6} \times 100\right) + \left(\frac{1}{9} \times (-50)\right) + \left(\frac{13}{18} \times 0\right)
]
[
\text{EV} = \frac{100}{6} - \frac{50}{9} = \frac{300 - 150}{18} = \frac{150}{18} \approx ₹8.33
]
Answer:
The expected profit per round is ₹8.33.
Note: If the actual problem differs, please provide the full question for a tailored solution.
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