Question

The probability that A, B, C solve a problem is ½, 2/3 and ¾. The probability that the problem is solved by only one of them is

• A. 5/12
• B. ¼
• C. 7/24
• D. 19/24

Answer 1

Answer: (B)

¼

Answer 2

Required probability

= P $( \overline { \mathrm { A } } \cap \overline { \mathrm { B } } \cap \overline { \mathrm { C } } ) + \mathrm { P } ( \overline { \mathrm { A } } \cap \mathrm { B } \cap \overline { \mathrm { C } } ) + \mathrm { P } ( \overline { \mathrm { A } } \cap \overline { \mathrm { B } } \cap \mathrm { C } )$

= P(1) P($\overline { \mathrm { A } }$) P(2) P( $\overline { \mathrm { C } }$ ) +

=$\frac { 1 } { 2 } \times \frac { 1 } { 3 } \times \frac { 1 } { 4 } + \frac { 1 } { 2 } \times \frac { 2 } { 3 } \times \frac { 1 } { 4 } + \frac { 1 } { 2 } \times \frac { 1 } { 3 } \times \frac { 3 } { 4 } = \frac { 6 } { 24 }$