1. The problem statement, all variables and given/known data http://imageshack.com/a/img546/5686/nqpn.jpg [Broken] I am looking for the probability of the current passing from the left to right given that there are 5 independent switches of probability p. However I cannot figure out the correct solution. 2. Relevant equations 3. The attempt at a solution Case I: Assume Switch E is closed so I have a probability of P((AB) or (CD))=P(AB)+P(CD)-P(AB and CD)=2p^2-p^4 Case II: Assume Switch E is opened so I have a probability of P((A or C) and (B or D))=(P(A)+P(C)-P(AC))(P(B)+P(D)-P(BD))=(2p-p^2)^2 so overall probability is (1-p)(2p^2-p^4)+p(2p-p^2)^2 which could be simplified to 2p^5-5p^4+2p^3+2p^2 however some friends of mine told be that it should be p^5-5p^4+2p^3+2p^2. I hope to know what's wrong in my calculation. Thanks!