Question

If A and B are events such that

$P ( A \cup B ) = 3 / 4 , P ( A \cap B ) = 1 / 4 , P ( \bar { A } ) = 2 / 3$ , then $P ( \bar { A } \cap B )$ is

• A. 5/12
• B. 3/8
• C. 5/8
• D. ¼

Answer 1

Answer: (A)

5/12

Answer 2

$P ( \bar { A } ) = \frac { 2 } { 3 }$ ⇒ $P ( A ) = \frac { 1 } { 3 }$.

∴ $P ( A \cap B ) = P ( A ) + P ( B ) - P ( A \cup B )$ ⇒ $\frac { 1 } { 4 } = \frac { 1 } { 3 } + P ( B ) - \frac { 3 } { 4 }$

⇒ $P ( B ) = \frac { 2 } { 3 }$ .

$P ( \bar { A } \cap B ) = P ( B ) - P ( A \cap B ) = \frac { 2 } { 3 } - \frac { 1 } { 4 } = \frac { 8 - 3 } { 12 } = \frac { 5 } { 12 }$.