A machine contains three independent components A,B and C. The machine operates only if every component operates.
a. (i) Given P(A)=0.90,P(B)=0.95 and P(C)=0.92, find the probability that the machine operates.
b. (ii) Find the probability that the machine fails to operate.
c. (iii) Calculate the probability that exactly one component fails during a run of the machine.