IIT-JEE Advanced 2022 Maths Paper 1 Problem 16

Problem

Two players, P₁ and P₂, 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 P₁ and P₂, respectively. If x > y, then P₁ scores 5 points and P₂ scores 0 points. If x = y, then each player scores 2 points. If x < y, then P₁ scores 0 points and P₂ scores 5 points. Let X_i and Y_i be the total scores of P₁ and P₂, respectively, after playing the i^th round.

Match the following.

List-1	List-2
(I) Probability of (X2 ≥ Y2) is	(P) 3/8
(II) Probability of (X2 > Y2) is	(Q) 11/16
(III) Probability of (X3 = Y3) is	(R) 5/16
(IV) Probability of (X3 > Y3) is	(S) 355/864
	(T) 77/432

Solution

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