CAT 2020 Slot 3: Quantitative Ability - Indian Game Probability Question
Problem Statement (Hypothetical Example):
In a traditional Indian dice game, players roll two six-sided dice. If the sum is 7 or 11, they win immediately. If the sum is 2, 3, or 12, they lose. Otherwise, the game continues to the next round. What is the probability of winning on the first roll?
Solution:
Total Possible Outcomes:
Rolling two dice has (6 \times 6 = 36) possible outcomes.
Winning Outcomes (Sum = 7 or 11):
Sum = 7: ((1,6), (2,5), (3,4), (4,3), (5,2), (6,1)) → 6 outcomes.
Sum = 11: ((5,6), (6,5)) → 2 outcomes.
Total Winning Outcomes: (6 + 2 = 8).
Probability Calculation:
[
P(\text{Win}) = \frac{\text{Winning Outcomes}}{\text{Total Outcomes}} = \frac{8}{36} = \frac{2}{9} \approx 22.22%.
]
Key Concept:
This tests classical probability involving independent events (dice rolls). Focus on enumerating favorable outcomes and dividing by total possibilities.
Common CAT 2020 Quant Traps & Tips:
Time Management: Prioritize high-weightage topics (e.g., probability, algebra).
Game Theory Scenarios: Look for problems involving optimal strategies or recursive probabilities (e.g., multi-round games).
Data Interpretation (DI): If the question involves game stats (e.g., player performance tables), use charts to identify trends.
Example DI Question (Hypothetical):
Given a table of Indian cricket players’ runs scored in T20s, calculate the median runs for players who scored above the average.
Steps:
Compute the average runs.
Filter players scoring above average.
Sort and find the median.
Final Answer:
The probability of winning on the first roll is (\boxed{\dfrac{2}{9}}).
Let me know if you need further clarification or additional examples!
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