Question

The probability of A, B, C solving a problem are $\frac { 2 } { 7 }$, $\frac { 3 } { 8 }$

respectively. If all the three try to solve the problem

simultaneously, the probability that exactly one of them will

solve it, is -

• A. $\frac { 25 } { 168 }$
• B. $\frac { 25 } { 56 }$
• C. $\frac { 20 } { 168 }$
• D. $\frac { 30 } { 168 }$

Answer 1

Answer: (B)

$\frac { 25 } { 56 }$

Answer 2

P(1) = $\frac { 1 } { 3 }$ ,P(2) = $\frac { 2 } { 7 }$ , P(3) = $\frac { 3 } { 8 }$

Required Prob. = P (1) P( $\overline { \mathrm { B } }$ ) P($\overline { \mathrm { A } }$)P(2) P(3) +

P($\overline { \mathrm { A } }$) P() P(3)

= $\frac { 1 } { 3 }$ $\left( 1 - \frac { 3 } { 8 } \right)$ +$\left( 1 - \frac { 1 } { 3 } \right)$

$\left( 1 - \frac { 2 } { 7 } \right)$ $\frac { 3 } { 8 }$