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 find the probability that not can solve it.

Explanation

Let three persons be A,B and C.
Clearly,the probabilities of solving the probalem by A, B and C are independent.
Given tht `P(A)=1//3,P(B)=1//4and P(C)=1//5.`
`therefore` P(none can solve the problem)
`P(A'nnB'nnC')`
`=P(A')nn(B')P(C')`
`=(1-P(A))(1-P(C))`
`=(1-(1)/(3))(1-(1)/(4))(1-(1)/(5))`
`=(2)/(3).(3)/(4).(4)/(5)=2/5`