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Question: The minimum value of P(A Č B), if P( \(\overline { \mathrm { B } }\) ) = {P(A Č B)}<sup>2</sup> is...

The minimum value of P(A Č B), if P( B‾\overline { \mathrm { B } } ) = {P(A Č B)}2 is

A

5−12\frac { \sqrt { 5 } - 1 } { 2 }

B

5+12\frac { \sqrt { 5 } + 1 } { 2 }

C

3−12\frac { \sqrt { 3 } - 1 } { 2 }

D

None of these

Answer

5−12\frac { \sqrt { 5 } - 1 } { 2 }

Explanation

Solution

P (AB)‾\overline { \left( \frac { A } { B } \right) } = = 1−xx2\frac { 1 - \mathrm { x } } { \mathrm { x } ^ { 2 } }  1 Ž x2 + x – 1  0

Žx ³ 5−12\frac { \sqrt { 5 } - 1 } { 2 } and x £ −1−52\frac { - 1 - \sqrt { 5 } } { 2 }

As x is +ve

\x ³ 5−12\frac { \sqrt { 5 } - 1 } { 2 }