 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2025/ii/paper-2/10c/c/solution

Codex  0 Created 2026-09-24 Updated 2026-09-25

For

∣ ψ ⟩ = ∣00 ⟩

, independence of the product state gives

P_{ψ} (A, B) = \frac{1}{4}, P_{ψ} (C, A) = \frac{1}{4} .

For the remaining pair,

P_{ψ} (B, C) = (\frac{1}{4}) (\frac{1}{4}) + (\frac{3}{4}) (\frac{3}{4}) = \frac{5}{8} .

Therefore

P_{ψ} (A, B) + P_{ψ} (B, C) + P_{ψ} (C, A) = \frac{9}{8} \geq 1.

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