Question

A bag contains 5 balls all of different colours (one of which is white) three persons A, B and C whose probabilities of speaking truth are $\frac { 1 } { 2 }$, $\frac { 2 } { 3 }$ and $\frac { 3 } { 4 }$ respectively assert that a ball drawn from the bag is white, the probability of truth of their assertion, is

• A. $\frac { 96 } { 97 }$
• B. $\frac { 24 } { 25 }$
• C. $\frac { 1 } { 20 }$
• D. $\frac { 6 } { 7 }$

Answer 1

Answer: (A)

$\frac { 96 } { 97 }$

Answer 2

P(5)= $\frac { \frac { 1 } { 2 } \times \frac { 2 } { 3 } \times \frac { 3 } { 4 } } { \frac { 1 } { 2 } \times \frac { 2 } { 3 } \times \frac { 3 } { 4 } + \left( \frac { 1 } { 4 } \right) ^ { 3 } \times \frac { 1 } { 2 } \times \frac { 1 } { 3 } \times \frac { 1 } { 4 } \times 4 }$= $\frac { 96 } { 97 }$