Answer
$P$(System A operates)= $71.2712$%
Work Step by Step
Event A: #1 component will operate properly.
Event B: #2 component will operate properly.
Event C: #3 component will operate properly.
All the events are independent.
$P$(all components operating properly) = $P$(A ∩ B ∩ C).
$P$(all components operating properly) = $P$(A) * $P$(B) * $P$(C)
$P$(all components operating properly) = $0.88\times0.91\times0.89$ (probabilities are given)
$P$(all components operating properly) = $71.2712$%
