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Choose the correct option.
If A and B are two events such that P(A) > 0 and P(B) ≠ 1, then P(A̅/B̅) is
If $A$ and $B$ are two events such that $P(A) > 0$ and $P(B) \neq 1$, then $P(\bar{A}/\bar{B})$ is
- (a)$1 - P(\bar{A}/B)$
- (b)$1 - P(A/B)$
- (c)$\frac{1 - P(A \cup B)}{P(\bar{B})}$
- (d)$\frac{P(\bar{A})}{P(B)}$
Answer
Answer
Correct option: (c)
Answer: (c) $\frac{1 - P(A \cup B)}{P(\bar{B})}$
$P(\bar{A}/\bar{B}) = \frac{P(\bar{A} \cap \bar{B})}{P(\bar{B})}$ and $P(\bar{A} \cap \bar{B}) = P\left(\overline{A \cup B}\right) = 1 - P(A \cup B)$.
Hence $P(\bar{A}/\bar{B}) = \frac{1 - P(A \cup B)}{P(\bar{B})}$.