Consider the circuit shown in figure. Each of its five relays is closed with the probability \(p\) independently of other relays.
Find the probability that a signal will pass through the circuit.
Find the probability that the relay \(E\) is open if it is known that the signal has passed through the circuit.
Figure 7 of the source (the circuit) is a bridge: from the input the line splits into an upper branch through relay \(A\) to an upper node and a lower branch through relay \(C\) to a lower node; the upper node is joined to the output through relay \(B\), the lower node is joined to the output through relay \(D\), and relay \(E\) joins the upper node to the lower node.