A machine will function only if all three of its independent subsystems A, B and C are operational. The probabilities that the individual subsystems are operational on a given day are
$P(A)=0.95,
P(B)=0.90,
P(C)=0.85.$
a. (i) Calculate the probability that the machine is operational on that day.
b. (ii) Hence, determine the probability that the machine fails on that day.