Q80 / 125 · BITSAT 2010 · Mathematics
If \(\mathrm{P}(\mathrm{A} \cup \mathrm{B})=\frac{2}{3}, \mathrm{P}(\mathrm{A} \cap \mathrm{B})=\frac{1}{6}\) and \(\mathrm{P}(\mathrm{A})=\frac{1}{3}\) then
- Correct answerAA and \(\mathrm{B}\) are independent events
- BA and \(\mathrm{B}\) are disjoint events
- CA and \(\mathrm{B}\) are dependent events
- DNone of these
Solution
\(\mathrm{P}(\mathrm{A} \cup \mathrm{B})=\mathrm{P}(\mathrm{A})+\mathrm{P}(\mathrm{B})-\mathrm{P}(\mathrm{AB})\)
\(\Rightarrow \frac{2}{3}=\frac{1}{3}+\mathrm{P}(\mathrm{B})-\frac{1}{6} \Rightarrow \mathrm{P}(\mathrm{B})=\frac{1}{2}\)
Now, \(\mathrm{P}(\mathrm{AB})=\mathrm{P}(\mathrm{A})~ \mathrm{P}(\mathrm{B}), \mathrm{A}\) and \(\mathrm{B}\) are independent events.
Hence, the correct answer is option: 'A'.