GATE EC 2024 Set 1 Q35 — Digital Communications

​​​​​A source transmits a symbol $s$, taken from $\{-4,0,4\}$ with equal probability, over an additive white Gaussian noise channel. The received noisy symbol $r$ is given by $r=s+w$, where the noise $w$ is zero mean with variance 4 and is independent of $s$. Using $Q(x)=\frac{1}{\sqrt{2 \pi}} \int_{x}^{\infty} e^{\frac{-t^{2}}{2}} d t$, the optimum symbol error probability is $\_\_\_\_\_\_$.