Two players, P 1 and P 2 , play a game against each other. In every round of the game, each player rolls a fair die once, where the six faces of the die have six distinct numbers. Let x and y denote the readings on the die rolled by P 1 and P 2 , respectively. If x y, then P 1 scores 5 p

Question

Two players, P 1 and P 2 , play a game against each other. In every round of the game, each player rolls a fair die once, where the six faces of the die have six distinct numbers. Let x and y denote the readings on the die rolled by P 1 and P 2 , respectively. If x > y, then P 1 scores 5 points and P 2 scores 0 point. If x = y, then each player scores 2 points. If x < y, then P 1 scores 0 point and P 2 scores 5 points. Let X i and Y i be the total scores of P 1 and P 2 , respectively, after playing the i th round. List-I List-II (I) Probability of (X 2 ≥ Y 2 ) is (P) 8 3 (II) Probability of (X 2 > Y 2 ) is (Q) 16 11 (III) Probability of (X 3 = Y 3 ) is (R) 16 5 (IV) Probability of (X 3 > Y 3 ) is (S) 864 355 (T) 432 77 The correct option is :

Accepted Answer

(I) → (Q); (II) → (R); (III) → (T); (IV) → (S)

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