Target Exam

CUET

Subject

Maths. Section B1

Chapter

Probability

Question:

If $A$ and $B$ are such events that $P(A) > 0$ and $P(B) \neq 1$, then $P(A' \mid B')$ is equal to

Options:

$1 - P(A \mid B)$

$1 - P(A' \mid B)$

$\frac{1 - P(A \cup B)}{P(B')}$

$P(A') \mid P(B')$

Correct Answer:

$\frac{1 - P(A \cup B)}{P(B')}$

Explanation:

The correct answer is Option (3) → $\frac{1 - P(A \cup B)}{P(B')}$ ##

$∵P(A) > 0$ and $P(B) \neq 1$

$∴P(A' \mid B') = \frac{P(A' \cap B')}{P(B')} = \frac{P(A \cup B)'}{P(B')} = \frac{1 - P(A \cup B)}{P(B')}$