Match List-I with List-II

Let A and B be any two events

Choose the correct answer from the options given below:

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

The correct answer is Option (3) → (A)-(III), (B)-(IV), (C)-(II), (D)-(I)

(A)

Complement of an event.

$A' \text{ denotes the complement of } A.$

$A\cup A' = S,\quad A\cap A' = \emptyset$

By finite additivity,

$P(A)+P(A')=P(S)=1$

Therefore

$P(A')=1-P(A)$

Match: (A) → (III)

(B)

Null (empty) event.

By the probability axioms, the empty set has probability zero:

$P(\emptyset)=0$

Match: (B) → (IV)

(C)

Conditional probability of A given B (requirement: $P(B)\neq 0$).

Definition:

$P(A\mid B)=\frac{P(A\cap B)}{P(B)}$

Equivalently $P(A\cap B)=P(A\mid B)\,P(B)$.

Match: (C) → (II)

(D)

Conditional probability of B given A (requirement: $P(A)\neq 0$).

Definition:

$P(B\mid A)=\frac{P(A\cap B)}{P(A)}$

Match: (D) → (I)