The following figures show some electrical circuits with switches on them (labeled 1, 2, and so on). Every switch works independently of others and can be at the position OFF (allowing the transmission of electricity) with a probability pi, i = 1, 2,…, or at the position ON, in which case the electricity cannot pass through.

If at the ends of each of the three circuits, we apply some voltage find, as a function of pi, the probability that electricity is transmitted through the circuit.