Solveeit Logo
Login

Question

Question: Three persons work independently on a problem. If the respective probabilities that they will solve ...

Three persons work independently on a problem. If the respective probabilities that they will solve it are 1/3, 1/4 and 1/5, then the probability that none can solve it

A

25\frac { 2 } { 5 }

B

35\frac { 3 } { 5 }

C

13\frac { 1 } { 3 }

D

None of these

Answer

25\frac { 2 } { 5 }

Explanation

Solution

Required probability

=(1−13)(1−14)(1−15)= \left( 1 - \frac { 1 } { 3 } \right) \left( 1 - \frac { 1 } { 4 } \right) \left( 1 - \frac { 1 } { 5 } \right) =23⋅34⋅45=25= \frac { 2 } { 3 } \cdot \frac { 3 } { 4 } \cdot \frac { 4 } { 5 } = \frac { 2 } { 5 }

=(1−13)(1−14)(1−15)= \left( 1 - \frac { 1 } { 3 } \right) \left( 1 - \frac { 1 } { 4 } \right) \left( 1 - \frac { 1 } { 5 } \right)

=23⋅34⋅45=25= \frac { 2 } { 3 } \cdot \frac { 3 } { 4 } \cdot \frac { 4 } { 5 } = \frac { 2 } { 5 }