#sequence-probability

An HMM has hidden states A, T, G, C, starts in each with probability $1/4$, and has transitions $A \to A$, $A \to T$, $T \to T$, $T \to G$, $G \to G$, $G \to C$, $C \to C$, $C \to A$, each with probability $1/2$. States A and G always emit 1; states T and C always emit 2. What probability does it assign to the output sequence 1, 2, 1, 2?