Question

If A and B are two events such that P(1) = $\frac { 1 } { 2 }$ and P(2) = $\frac { 2 } { 3 }$ ,

then -

• A. P (A Č B) ³ $\frac { 1 } { 3 }$
• B. P (A Ē) £ $\frac { 1 } { 2 }$
• C. $\frac { 1 } { 6 }$ £ P(A Ē B) £ $\frac { 1 } { 2 }$
• D. $\frac { 1 } { 6 }$ £ P( $\overline { \mathrm { A } }$ Ē B) £ $\frac { 3 } { 4 }$

Answer 1

Answer: (A)

P (A Č B) ³ $\frac { 1 } { 3 }$

Answer 2

We have,

P (A Č B) ³ max {P (1), P (2)} = $\frac { 1 } { 2 }$.

Also, P (A Ē$\frac { 1 } { 6 }$=$\frac { 1 } { 3 }$ and, P

( $\overline { \mathrm { A } }$ Ē B) = P (2) – P (A Ē B) £ $\frac { 2 } { 3 }$ – $\frac { 1 } { 6 }$= $\frac { 1 } { 2 }$ .

Hence,

$\frac { 2 } { 3 }$ – $\frac { 1 } { 2 }$ £ P ( $\overline { \mathrm { A } }$ Ē B) £ $\frac { 1 } { 6 }$ Ž $\frac { 1 } { 6 }$ £

P ( $\overline { \mathrm { A } }$ Ē B) £ $\frac { 1 } { 2 }$.

Hence (1) is the correct answer