If 2P(A) = P(B) = 5/13 and P(A|B) = 2/5, then P(A B) is Option 1: 1/13 Option 2: 2/13 Option 3: 3/13 Option 4: 4/13

Answer: 2/13. Solution: Given 2P(A) = P(B) = 5/13 From this: P(B) = 5/13 2P(A) = 5/13 P(A) = 5/26 Also given: P(A, B) = 2/5 The conditional probability formula is: P(A, B) = (P(A B))/(P(B)) Rearranging for P(A B): P(A B) = P(A, B) x P(B) P(A B) = 2/5 x 5/13 P(A B) = 10/65 P(A B) = 2/13 Therefore, P(A B) = 2/13

Algebra

Probability

Medium

core

If $2P(A) = P(B) = \frac{5}{13}$ and $P(A|B) = \frac{2}{5}$ , then $P(A \cap B)$ is

$\frac{1}{13}$

$\frac{2}{13}$

$\frac{3}{13}$

$\frac{4}{13}$

✅ Correct Option: 2

Given $2P(A) = P(B) = \frac{5}{13}$

From this:

$P(B) = \frac{5}{13}$

$2P(A) = \frac{5}{13}$

$P(A) = \frac{5}{26}$

Also given: $P(A|B) = \frac{2}{5}$

The conditional probability formula is:

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

Rearranging for $P(A \cap B)$ :

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

$P(A \cap B) = \frac{2}{5} \times \frac{5}{13}$

$P(A \cap B) = \frac{10}{65}$

$P(A \cap B) = \frac{2}{13}$

Therefore, $P(A \cap B) = \frac{2}{13}$

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If 2P(A)=P(B)=5132P(A) = P(B) = \frac{5}{13}2P(A)=P(B)=135​ and P(A∣B)=25P(A|B) = \frac{2}{5}P(A∣B)=52​, then P(A∩B)P(A \cap B)P(A∩B) is

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CUET Mathematics Past Year Questions (Topic-Wise)

If $2P(A) = P(B) = \frac{5}{13}$ and $P(A|B) = \frac{2}{5}$ , then $P(A \cap B)$ is