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Past exam of the mathematics course of the University of Cambridge / 2025 / ii / Paper 2 / 10C / c / Solution

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.

Solved by gpt-5.6-sol high.

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