About this question

Non-Transitive Dice

Hard · Conditional Probability · Quant Trader interview question · probability, game-theory, conditional-probability

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?