JEE Advanced 2022 Paper 1 Mathematics Q16

Mathematics

Problem

Two players P₁ and P₂ play a game. In every round each rolls a fair die once. If x>y, P₁ scores 5 and P₂ scores 0; if x=y, each scores 2; if x<y, P₁ scores 0 and P₂ scores 5. Let Xᵢ and Yᵢ be their total scores after the i-th round. Match List-I: (I) P(X₂≥Y₂); (II) P(X₂>Y₂); (III) P(X₃=Y₃); (IV) P(X₃>Y₃), with List-II: (P)3/8; (Q)11/16; (R)5/16; (S)355/864; (T)77/432.

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