Jee Advanced
Probability
JEE Advanced 2022 Paper 1 Online
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 \(i^{\text {th }}\) round.
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| List-I | List-II |
|---|---|
| (I) Probability of \(\left(X_{2} \geq Y_{2}\right)\) is | (P) \(\frac{3}{8}\) |
| (II) Probability of \(\left(X_{2}>Y_{2}\right)\) is | (Q) \(\frac{11}{16}\) |
| (III) Probability of \(\left(X_{3}=Y_{3}\right)\) is | (R) \(\frac{5}{16}\) |
| (IV) Probability of \(\left(X_{3}>Y_{3}\right)\) is | (S) \(\frac{355}{864}\) |
| (T) \(\frac{77}{432}\) |
The correct option is: