A) A and B are independent
B) \[P\left( \frac{{{A}'}}{B} \right)=\frac{3}{4}\]
C) \[P\left( \frac{{{B}'}}{{{A}'}} \right)=\frac{1}{2}\]
D) All of these
Correct Answer: D
Solution :
\[P\left( \frac{B}{A} \right)=\frac{1}{2}\]\[\Rightarrow \,\frac{P(B\cap A)}{P(A)}=\frac{1}{2}\]\[\Rightarrow P(B\cap A)=\frac{1}{8}\] \[P\left( \frac{A}{B} \right)=\frac{1}{4}\]\[\Rightarrow \,\frac{P(A\cap B)}{P(B)}=\frac{1}{4}\] \[\Rightarrow P(B)\,=\frac{1}{2}\] \[P(A\cap B)=\frac{1}{8}\,=P(A).\,P(B)\,\] \[\therefore \] Events A and B are independent. Now, \[P\,\left( \frac{{{A}'}}{B} \right)=\frac{P({A}'\cap B)}{P(B)}=\frac{P({A}')\,P(B)}{P(B)}=\frac{3}{4}\] and \[P\,\left( \frac{B'}{A'} \right)=\frac{P(B'\cap A')}{P(A')}=\frac{P(B')\,P(A')}{P(A')}=\frac{1}{2}\].You need to login to perform this action.
You will be redirected in
3 sec