CUET UG 2025 — Mathematics Algebra

2025mcqmedium

If A and B are independent events such that $P(A|B) = \frac{1}{3}$ and $P(B) = \frac{1}{2}$ , then the value of $P(A \cap B)$ is equal to

Official previous-year question

Held on 13 May 2025 · Verified 13 Jul 2026.

Options

A
$\frac{1}{3}$
B
$\frac{1}{6}$
C
$\frac{1}{12}$
D
$\frac{1}{2}$

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Solution

Events $A$ and $B$ are independent, with $P(A|B) = \frac{1}{3}$ and $P(B) = \frac{1}{2}$ .

For independent events, $P(A|B) = P(A)$ .

(Translation: If $A$ and $B$ don't affect each other, then the probability of $A$ given $B$ has happened is just the probability of $A$ )

Since $P(A|B) = \frac{1}{3}$ , this means $P(A) = \frac{1}{3}$ .

For independent events:

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

Substituting the values:

$P(A \cap B) = \frac{1}{3} \times \frac{1}{2}$

$P(A \cap B) = \frac{1}{6}$

Alternatively, using the conditional probability formula:

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

Rearranging:

$P(A \cap B) = P(A|B) \times P(B)$

$P(A \cap B) = \frac{1}{3} \times \frac{1}{2}$

$P(A \cap B) = \frac{1}{6}$

Therefore, $P(A \cap B) = \frac{1}{6}$ .

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Solution

Events $A$ and $B$ are independent, with $P(A|B) = \frac{1}{3}$ and $P(B) = \frac{1}{2}$ .

For independent events, $P(A|B) = P(A)$ .

(Translation: If $A$ and $B$ don't affect each other, then the probability of $A$ given $B$ has happened is just the probability of $A$ )

Since $P(A|B) = \frac{1}{3}$ , this means $P(A) = \frac{1}{3}$ .

For independent events:

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

Substituting the values:

$P(A \cap B) = \frac{1}{3} \times \frac{1}{2}$

$P(A \cap B) = \frac{1}{6}$

Alternatively, using the conditional probability formula:

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

Rearranging:

$P(A \cap B) = P(A|B) \times P(B)$

$P(A \cap B) = \frac{1}{3} \times \frac{1}{2}$

$P(A \cap B) = \frac{1}{6}$

Therefore, $P(A \cap B) = \frac{1}{6}$ .

CUET UG 2025 — Mathematics Algebra

Options

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Solution

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CUET UG 2025 — Mathematics Algebra

Options

Did you get this right?

Solution

Your note

CUET UG Algebra in other years

More CUET UG Algebra questions

Other Mathematics topics for CUET UG

Calculus

Applied-Mathematics

Statistics & Applications

Geometry

Arithmetic

Coordinate Geometry

Keep practicing Algebra