Find the probability of a functioning circuit 
I keep getting that
$$P(\text{Circuit works}) = P(\geq\text{1 of subcircuit 1}) +P(\geq\text{1 of subcircuit 2}) +P(\geq\text{1 of subcircuit 3})  $$
$$= (0.9*0.1^2 + 0.9^2*0.1 + 0.9^3)*(0.95^2 + 0.95*0.05)*(0.99) = 0.770$$
But this is the wrong answer

For example, the probability that the central pair of parallel devices fails is equal to $(1-0.95)*(1-0.95)$; so the probability that the central pair works is $1-(1-0.95)*(1-0.95)$, and so on. 
