Q105 / 180 · COMEDK 2014 · Mathematics
If the occurrence of an event $A$ implies that occurrence of an event $B$, the $P\left(A^{C} \cap B^{C}\right)$ is equal to
- Correct answerA$P\left(B^{C}\right)$
- B$P\left(A^{C}\right) P\left(B^{C}\right)$
- C$P\left(A^{C}\right)$
- D$1-P(A \cap B)$
Solution
$P\left(A^{C} \cap B^{C}\right)=P\left((A \cup B)^{C}\right)=1-P(A \cup B)$
Since, probability of occurrence of an event A implies the occurrence of event $B$,
$$
\begin{aligned}
&\therefore A \subset B \Rightarrow A \cup B=B \\
&\Rightarrow P\left(A^{C} \cap B^{C}\right)=1-P(B)=P\left(B^{C}\right)
\end{aligned}
$$
Hence, the correct answer is option: 'A'.