Question

It is given that the events A and B are such that P(1) = $\frac { 1 } { 4 }$ ,

P $\left( \frac { \mathrm { A } } { \mathrm { B } } \right)$ =$\frac { 1 } { 2 }$,P= $\frac { 2 } { 3 }$ then P(2) =

• A. $\frac { 1 } { 6 }$
• B. $\frac { 1 } { 3 }$
• C. $\frac { 2 } { 3 }$
• D. $\frac { 1 } { 2 }$

Answer 1

Answer: (B)

$\frac { 1 } { 3 }$

Answer 2

P = $\frac { \mathrm { P } ( \mathrm { A } \cap \mathrm { B } ) } { \mathrm { P } ( \mathrm { B } ) }$ Ž $\frac { 1 } { 2 }$ = $\frac { 1 / 6 } { \mathrm { P } ( \mathrm { B } ) }$

Ž P(2) = $\frac { 1 / 6 } { 1 / 2 }$ = $\frac { 2 } { 6 } = \frac { 1 } { 3 }$

P $\left( \frac { B } { \mathrm {~A} } \right)$ = $\frac { \mathrm { P } ( \mathrm { A } \cap \mathrm { B } ) } { \mathrm { P } ( \mathrm { A } ) }$Ž $\frac { 2 } { 3 }$ = $\frac { x } { 1 / 4 }$

Ž x = $\frac { 1 } { 4 } \cdot \frac { 2 } { 3 } = \frac { 1 } { 6 }$