Question

For two events A and B, if $P ( A ) = P \left( \frac { A } { B } \right) = \frac { 1 } { 4 }$ and $P \left( \frac { B } { A } \right) = \frac { 1 } { 2 }$ then

• A. A and B are independent
• B. $P \left( \frac { A ^ { \prime } } { B } \right) = \frac { 3 } { 4 }$
• C. $P \left( \frac { B ^ { \prime } } { A ^ { \prime } } \right) = \frac { 1 } { 2 }$
• D. All of the above

Answer 1

Answer: (D)

All of the above

Answer 2

are independent as $P ( A ) = P \left( \frac { A } { B } \right)$

$P \left( \frac { A ^ { \prime } } { B } \right) = 1 - \frac { 1 } { 4 } = \frac { 3 } { 4 }$ as $A , B$ are independent

$\Rightarrow A ^ { \prime } , B$ are independent.

$P \left( \frac { B ^ { \prime } } { A ^ { \prime } } \right) = P \left( B ^ { \prime } \right) = 1 - \frac { 1 } { 2 } = \frac { 1 } { 2 }$