Let a pair of dice be thrown and the random variable X be the sum of the numbers that appear on the two dice.

Match List-I with List-II

Choose the correct answer from the options given below.

(A)-(III), (B)-(IV), (C)-(II), (D)-(I)

The correct answer is Option (4) → (A)-(III), (B)-(IV), (C)-(II), (D)-(I)

For two fair dice, total outcomes = $36$.

$X=4$: outcomes $(1,3),(2,2),(3,1)$ → $3$ outcomes → $P=\frac{3}{36}=\frac{1}{12}$ → (III).

$X=5$: outcomes $(1,4),(2,3),(3,2),(4,1)$ → $4$ outcomes → $P=\frac{4}{36}=\frac{1}{9}$ → (IV).

$X=6$: outcomes $(1,5),(2,4),(3,3),(4,2),(5,1)$ → $5$ outcomes → $P=\frac{5}{36}$ → (II).

$X=7$: outcomes $(1,6),(2,5),(3,4),(4,3),(5,2),(6,1)$ → $6$ outcomes → $P=\frac{6}{36}=\frac{1}{6}$ → (I).

Final answer: (A)–(III), (B)–(IV), (C)–(II), (D)–(I)