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Q.

Two players, P1and 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  P1and P2,  respectively. If x > y, then P1 scores 5 points and  P2 scores 0 point. If x = y, then each player score 2 points. If x < y, then P1 scores 0 point and  P2  scores 5 points. Let  Xiand Yi be the total scores of  P1and P2, respectively, after playing the ith round.

 List – I List – II
I) Probability of  (X2Y2)   isP) 38
II) Probability of  (X2>Y2)  isQ) 1116
III) Probability of   (X3=Y3) isR) 516
IV) Probability of  (X3>Y3)   isS) 355864
  T) 77432

The correct option is

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An Intiative by Sri Chaitanya

a

IQ;IIR;IIIT;IVP

b

IP;IIR;IIIQ;IVS

c

IQ;IIR;IIIT;IVS

d

IP;IIR;IIIQ;IVT

answer is A.

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Detailed Solution

(1)
S={(1,1),(1,2),(1,3)...,(1,6)          (2,1)...,(2,2),(2,3)...,(2,6)          (6,1),(6,2),(6,3)...,(6,6)}
P(P1)=512=P(P2),P(D)=16 i)P(X2Y2)=P(P1).P(P1)+2P(P1).P(P1)+P(D).P(D)+2P(P1).P(D) =512×512+2512512+16×16+2.512.16=1116 ii)P(X2>Y2)=P(P1).P(P1)+2P(P1).P(D)=516 iii)P(X3=Y3)=3P(P1).P(D).P(P2)+P(D).P(D).P(D) =77432 iv)P(X3>Y3)=P(P1).P(P1).P(P1)+3P(P1).P(P1).P(P2)+3P(P1).P(P1).P(D)+3P(P1).P(D).P(D) =355864 

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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 point. If x = y, then each player score 2 points. If x < y, then P1 scores 0 point and  P2  scores 5 points. Let  Xi and Yi be the total scores of  P1 and P2, respectively, after playing the ith round. List – I List – III) Probability of  (X2≥Y2)   isP) 38II) Probability of  (X2>Y2)  isQ) 1116III) Probability of   (X3=Y3) isR) 516IV) Probability of  (X3>Y3)   isS) 355864  T) 77432The correct option is