Answer
$P$(System B operates properly)= $96.39$%.
Work Step by Step
Event A: Subsystem C works properly.
Event B: Subsystem D works properly.
$P$(A) = $P$(#1 component operates) ∩ $P$(#2 component operates).
$P$(A) = $0.9\times0.9$
$P$(A) = $81$%.
Similarly, $P$(B) = $81$%.
$P$(any subsystem works) = $P$( A or B) = $P$(A U B)
$P$(A U B) = $P$(A) +$P$(B) -$P$(A ∩ B).
$P$(A U B) = $0.81 + 0.81 -$ $P$(A) * $P$(B).
$P$(A U B) = $0.81 + 0.81 -(0.81*0.81)$.
$P$(A U B) = $0.81 + 0.81 -(0.6561)$
$P$(A U B) = $0.9639$%.
