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.