In coding theory, a binary symmetric channel is an idealized model of a communication 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 1's and 0's 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 < 1/2 be the probability of an error occuring. 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.