Match List-I with List-II Let A and B be any two events, List-I, List-II, (A) P(A'), (I) (P(A B))/(P(A)); P(A) ≠ 0, (B) P(), (II) (P(A B))/(P(B)); P(B) ≠ 0, (C) P(A B), (III) 1 - P(A), (D) P(B A), (IV) 0, Choose the correct answer from the options given below: Option 1: (A) - (III), (B) - (IV), (C) - (I), (D) - (II) Option 2: (A) - (IV), (B) - (III), (C) - (I), (D) - (II) Option 3: (A) - (III), (B) - (IV), (C) - (II), (D) - (I) Option 4: (A) - (IV), (B) - (III), (C) - (II), (D) - (I)

Answer: (A) - (III), (B) - (IV), (C) - (II), (D) - (I). Solution: P(A') = 1 - P(A) This is the complement rule. (A) (III) P() = 0 is the empty set (no outcome), so the probability is always 0. (B) (IV) P(A, B) = (P(A B))/(P(B));\ P(B) ≠ 0 In P(A, B), the event after the bar (here B) goes in the denominator. (C) (II) P(B, A) = (P(A B))/(P(A));\ P(A) ≠ 0 In P(B, A), the event after the bar (here A) goes in the denominator. (D) (I) (A) (III), (B) (IV), (C) (II), (D) (I)

Algebra

Probability

Medium

core

Match List-I with List-II

Let A and B be any two events

List-I List-II
(A) $P(A')$ (I) $\frac{P(A \cap B)}{P(A)}; P(A) \neq 0$
(B) $P(\phi)$ (II) $\frac{P(A \cap B)}{P(B)}; P(B) \neq 0$
(C) $P(A\vert B)$ (III) $1 - P(A)$
(D) $P(B\vert A)$ (IV) 0

Choose the correct answer from the options given below:

List-I	List-II
(A) $P(A')$	(I) $\frac{P(A \cap B)}{P(A)}; P(A) \neq 0$
(B) $P(\phi)$	(II) $\frac{P(A \cap B)}{P(B)}; P(B) \neq 0$
(C) $P(A\vert B)$	(III) $1 - P(A)$
(D) $P(B\vert A)$	(IV) 0

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

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

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

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

✅ Correct Option: 3

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

This is the complement rule.

$(A) \to (III)$

$P(\phi) = 0$

$\phi$ is the empty set (no outcome), so the probability is always 0.

$(B) \to (IV)$

$P(A|B) = \dfrac{P(A \cap B)}{P(B)};\ P(B) \neq 0$

In $P(A|B)$ , the event after the bar (here $B$ ) goes in the denominator.

$(C) \to (II)$

$P(B|A) = \dfrac{P(A \cap B)}{P(A)};\ P(A) \neq 0$

In $P(B|A)$ , the event after the bar (here $A$ ) goes in the denominator.

$(D) \to (I)$

$(A) \to (III),\quad (B) \to (IV),\quad (C) \to (II),\quad (D) \to (I)$

2026: 18 May Shift 2

If A and B are independent events such that $P(A)=\dfrac{1}{2}$ , $P(A\cup B)=\dfrac{3}{5}$ and $P(B)=p$ , then value of p is:

2025: 19 May Shift 1

If A and B are independent events, then which of the following statements are TRUE?

(A) $P(A \cap B) = P(A).P(B)$

(B) $P(A \cap B) = P(A) - P(B)$

(D) $P(A \cap B) = P(A). P(B|A)$

Choose the correct answer from the options given below:

2026: 19 May Shift 2

A beg contains 4 white and 6 red balls. Four balls are drawn at random, then match the probability of the numbers of white balls drawn. Where P(E) denotes the probability of an event E.

Then Match List-I with List-II

LIST-I		LIST-II
A.	P (no white ball)	I.	$\frac{8}{21}$
B.	P (all white balls)	II.	$\frac{1}{14}$
C.	P (one white ball)	III.	$\frac{6}{14}$
D.	P (two white balls)	IV.	$\frac{1}{210}$

Choose the correct answer from the options given below:

2025: 26 May Shift 2

A and B throw a die alternatively till one of them gets 3 or 6 and wins the game. If B starts the game, then the probability of winning the game by A is

2025: 3 June Shift 1

If A and B are independent events, then which of the following is not true?

2022: 6 Aug Shift 2

The probability that the study time of students is not more than one hour.

Solution

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