The probability of each resistor being turned on is 0.5, and the probability of being turned off is also 0.5.

When connected in parallel, as long as one circuit can be connected, only when both resistors are not connected, the circuits are not connected.

The probability of circuit connectivity = 1- The disconnected case and the disconnected case are 0.5*0.5.

1-0.5*0.5=0.75

The same is true for three parallel connections.

1-0.5*0.5*0.5=0.875