Non-Transitive Dice - Quant Trader Interview Question
Difficulty: Hard
Category: Conditional Probability
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Topics: probability, game-theory, conditional-probability
Problem Description
You are presented with a set of three dice: A, B, and C. Each die has six faces with integer values. The dice are non-transitive, meaning the following probabilities hold:
$P(A > B) > \frac{1}{2}$
$P(B > C) > \frac{1}{2}$
$P(C > A) > \frac{1}{2}$
Which of the following sets of dice satisfy these conditions?
Die A: 2, 2, 4, 4, 9, 9
Die B: 1, 1, 6, 6, 8, 8
Die C: 3, 3, 5, 5, 7, 7
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