This paper investigates the error probability of several decoding methods for a source code with decoder side information, where the decoding methods are: 1) symbol-wise maximum a posteriori decoding, 2) successive-cancellation decoding, and 3) stochastic successive-cancellation decoding. The proof of the effectiveness of a decoding method is reduced to that for an arbitrary decoding method, where `effective' means that the error probability goes to zero as $n$ goes to infinity. Furthermore, we revisit the polar source code showing that stochastic successive-cancellation decoding, as well as successive-cancellation decoding, is effective for this code.