In coding theory, a binary symmetric channel is an idealized model of a communications channel that sends bits. In a BSC, the probability of a 1 becoming a 0 and of a 0 becoming a 1 are assumed to be the same. Since 1s and 0s may be represented very differently (as a pulse and absence of a pulse, for instance), this assumption is often not valid in practical situations. However, this assumption makes analysis much easier.
Formally, let p < ½ be the probability of an error occurring. Then the probability of a bit sent over a BSC being correctly received is (1-p), and this probability is independent of what bit is sent.
(copied from Everything2 and posted here by the original author, Ryan Gabbard (elwethingol of Everything2))