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## Homework Statement

http://imageshack.com/a/img546/5686/nqpn.jpg

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.

## Homework Equations

## 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!

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