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 &nb

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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 &#62; y , then P 1  scores 5  points and P 2  scores 0  point. If x = y , then each player scores  2 points. If x &#60; 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 &#8805; Y 2  is P 3 8 II Probability of  X 2 &#62; Y 2  is Q 11 16 III Probability of  X 3 = Y 3  is R 5 16 IV Probability of  X 3 &#62; Y 3  is S 355 864     T 77 432 The correct option is:

Quantrex Academy · Accepted Answer

Correct answer: A. I &#8594; Q ; II &#8594; R ; III &#8594; T ; IV &#8594; S

Given, P (draw in 1 round) = 6 36 = 1 6 P (win in 1 round) = 1 2 1 - 1 6 = 5 12 P (loss in 1 round) = 5 12 Now finding the probability of all we get, P X 2 &#62; Y 2 = P 10 , 0 + P 7 , 2 = 5 12 &#215; 5 12 + 5 12 &#215; 1 6 &#215; 2 = 45 144 = 5 16 &#8594; R P X 2 = Y 2 = P 5 , 5 + P 4 , 4 = 5 12 &#215; 5 12 &#215; 2 + 1 6 &#215; 1 6 = 25 + 2 72 = 3 8 P X 2 &#8805; Y 2 = 5 16 + 3 8 = 11 16 &#8594; Q P X 3 = Y 3 = P 6 , 6 + P 7 , 7 = 1 6 &#215; 6 &#215; 6 + 5 12 &#215; 1 6 &#215; 5 12 &#215; 6 = 2 432 + 75 432 = 77 432 &#8594; T P X 3 &#62; Y 3 = 1 2 1 - 77 432 = 355 864 &#8594; S

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