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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 reading on the dice rolled by \( P_{1} \) and \( P_{2} \) respectively. If \( xy \) then \( P_{1} \) score 5 points and \( P_{2} \) scores 0 point. If \( x=y \), then each player scores 2 points. If \( xy \), 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.
List-I
(I) Probability \( \left(X_{2} \geq Y_{2}\right) \) is
(II) Probability \( \left(X_{2}Y_{2}\right) \) is
(III) Probability \( \left(X_{3}=Y_{3}\right) \) is
(IV) Probability \( \left(X_{3}Y_{3}\right) \) is
List-II
(P) \( \frac{3}{8} \)
(Q) \( \frac{11}{16} \)
(R) \( \frac{5}{16} \)
(S) \( \frac{355}{864} \)
(T) \( \frac{77}{432} \)
The correct option is:
(a) (I) \( \rightarrow \) (Q); (II) \( \rightarrow \) (R); (III) \( \rightarrow \) (T); (IV) \( \rightarrow(\mathrm{S}) \)
(b) (I) \( \rightarrow \) (Q); (II) \( \rightarrow \) (R); (III) \( \rightarrow \) (T); (IV) \( \rightarrow \) (T)
(c) (I) \( \rightarrow \) (P); (II) \( \rightarrow \) (R); (III) \( \rightarrow \) (Q); (IV) \( \rightarrow \) (S)
(d) (I) \( \rightarrow \) (P); (II) \( \rightarrow \) (R); (III) \( \rightarrow \) (Q); (IV) \( \rightarrow \) (T)
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