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

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
  1. $1-P(A \mid B)$
  2. $1-P(\bar{A} \mid B)$
  3. $\frac{1-P(A \cup B)}{P(\bar{B})}$
  4. $\frac{P(\bar{A})}{P(\bar{B})}$

Solution

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

Asked in: AP EAMCET 2022 (05 Jul Shift 1)

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