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Question: Answered & Verified by Expert
If $A$ and $B$ are two events such that $P(B) \neq 0$ and $P(B) \neq 1$, then $P(\bar{A} \mid \bar{B})$ is
MathematicsProbabilityAP EAMCETAP EAMCET 2022 (05 Jul Shift 1)
Options:
  • A $1-P(A \mid B)$
  • B $1-P(\bar{A} \mid B)$
  • C $\frac{1-P(A \cup B)}{P(\bar{B})}$
  • D $\frac{P(\bar{A})}{P(\bar{B})}$
Solution:
2542 Upvotes Verified Answer
The correct answer is: $\frac{1-P(A \cup B)}{P(\bar{B})}$
$P(\bar{A} \mid \bar{B})=\frac{P(\bar{B} \cap \bar{A})}{P(B)}=\frac{1-P(A \cup B)}{P(B)}$

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