A) \[\frac{2}{3}\]
B) \[\frac{1}{2}\]
C) \[\frac{1}{6}\]
D) \[\frac{1}{3}\]
Correct Answer: D
Solution :
\[P\left( A \right)=\frac{1}{4}\] \[P\left( \frac{A}{B} \right)=\frac{P\left( A\cap B \right)}{P\left( B \right)}\Rightarrow \frac{1}{2}=\frac{P\left( A\cap B \right)}{P\left( B \right)}\] ? (i) \[P\left( \frac{B}{A} \right)=\frac{P\left( A\cap B \right)}{P\left( A \right)}\Rightarrow \frac{2}{3}=\frac{P\left( A\cap B \right)}{1/4}\]\[\Rightarrow P\left( A\cap B \right)=\frac{1}{6}\]. Putting the value of \[P\left( A\cap B \right)\] in (i) \[\Rightarrow P\left( B \right)=2\times \frac{1}{6}=\frac{1}{3}\]You need to login to perform this action.
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