Suppose a binary message is transmitted through a noisy channel. The transmitted signal $S$ has uniform probability to be either $1$ or $−1$, the noise $N$ follows normal distribution $N(0,4)$ and the received signal is $R=S+N$ . Assume the receiver conclude the signal to be $1$ when $R>=0$ and $-1$ when $R<0$ .
What is the error probability if we send the same signal three times (with amplitude 1), and take majority for conclusion? For example, if three received signal was concluded $1, −1, 1$ by receiver, we determine the transmitted signal to be $1$.
I have knowledge about normal distribution but I have absolutely no clue of approaching this problem.