Solution
= Solution
By the Born rule,
$$
P_\psi(A,B)=|\langle a_0b_0|\psi\rangle|^2
+|\langle a_1b_1|\psi\rangle|^2,
$$
$$
P_\psi(B,C)=|\langle b_0c_0|\psi\rangle|^2
+|\langle b_1c_1|\psi\rangle|^2,
$$
and
$$
P_\psi(C,A)=|\langle c_0a_0|\psi\rangle|^2
+|\langle c_1a_1|\psi\rangle|^2.
$$
Each is the expectation of the projector onto the span of the two displayed matching-label product states.