**Given: **let A ,B and C be the three components of a machine which works only if all its three compenents function.

the probabilities of the failures of A,B and C respectively is given i.e,

P(A) = 0.14 ,P(B) = 0.10 and P(C) = 0.05

\(\Rightarrow\) P(\(\overline A\)) = = 0.86 and P(\(\overline B\)) = 0.90 and P(\(\overline C\)) = 0.95

**To Find: **The probability that the machine will fail.

Here, P(the machine will fail) = 1 – P(the machine will function)

= 1 – P(all three components are working)

**Therefore, **The probability that the machine will fail is 0.2647.