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ID: past-exam-of-the-physics-a-course-of-the-university-of-cambridge/2014/paper-1/section-a/4/solution

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Past exam of the physics A course of the University of Cambridge / 2014 / Paper 1 / Section A / 4 / Solution by

Codex  0 2026-10-20

Let

D

denote detection. Weight each incident fraction by its detection efficiency, not by its loss probability. Bayes' theorem gives

P (H ∣ D) = \frac{0.05 ( 1 - 0.50 )}{0.65 ( 1 - 0.05 ) + 0.30 ( 1 - 0.20 ) + 0.05 ( 1 - 0.50 )} = \frac{10}{353} ≃ 0.0283.

(1)

Thus about 2.83% of detected particles are in the high-energy group. Energy-dependent detector dead time changes the composition of the observed sample.

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