Let X denote the number of hours you play during a randomly selected day. The probability that X can values x has the following form, where c is some constant.

$P(X=x)= \begin{cases}0.1&, & \text { if } x=0 \\ c x&, & \text { if } x=1 \text { or } x=2 \\ c(5-x)&, & \text { if } x=3 \text { or } x=4 \\ 0&, & \text { otherwise }\end{cases}$

Match List-I with List-II:

Choose the correct answer from the options given below:

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

The correct answer is Option (2) → (A) - (IV), (B) - (III), (C) - (II), (D) - (I)

$∑P(X)=1$

$0.1+c+2c+c(5-3)+c(5-4)+0=1$

$0.1+3c+2c+c=1$

$6c=0.9⇒c=0.15$

(A) c → (IV) 0.15

(B) $P(X≤2)=0.1+c+2c=0.55$ (III)

(C) $P(X=2)=2c=0.30$ (II)

(D) $P(X≥2)=2c+c=0.75$ (I)