Solution
= Solution
For the real Bell state $|\phi^+\rangle$, real one-qubit <vectors> satisfy
$$
\langle x_jy_j|\phi^+\rangle
=\frac1{\sqrt2}\langle x_j|y_j\rangle.
$$
For each adjacent pair $(A,B)$, $(B,C)$, and $(C,A)$, the two same-label overlaps have magnitude $1/2$. Hence every matching-label probability is
$$
P_{\phi^+}(X,Y)=\frac12\left(\frac14+\frac14\right)=\frac14.
$$
It follows that
$$
\boxed{P_{\phi^+}(A,B)+P_{\phi^+}(B,C)+P_{\phi^+}(C,A)=\frac34.}
$$