A binary bit is transmitted into n channels, each with its own probability of error (p1,p2,..pn). At the receiver end, n bits are received from n channels, with a total combination of 2^n possibilities.
At receiver, there is a decision making body which operates on a majority rule. For example for 5 channels, if the received bits (32 combinations) have 3 or more "1/0", it will decide that bit to be used.
I wanted to obtain P(error) in terms of (p1,p2....pn) for such a system. How can I obtain a generic mathematical expression for such system?