Question

If A and B are two independent events such that

$P \left( A \cap B ^ { \prime } \right) = \frac { 3 } { 25 }$ and then $P ( A ) =$

• A. $\frac { 1 } { 5 }$
• B. $\frac { 3 } { 8 }$
• C. $\frac { 2 } { 5 }$
• D. $\frac { 4 } { 5 }$

Answer 1

Answer: (A)

$\frac { 1 } { 5 }$

Answer 2

Since events are independent.

So, $P \left( A \cap B ^ { \prime } \right) = P ( A ) \times P \left( B ^ { \prime } \right) = \frac { 3 } { 25 }$

$\Rightarrow P ( A ) \times \{ 1 - 2 P ( B ) \} = \frac { 3 } { 25 }$ .....(i)

Similarly, $P ( B ) \times \{ 1 - P ( A ) \} = \frac { 8 } { 25 }$ .....(ii)

On solving (i) and (ii), we get $P ( A ) = \frac { 1 } { 5 }$ and $\frac { 3 } { 5 }$.