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ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2008/paper-2/11/d/iv/solution

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Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge / 2008 / Paper 2 / 11 / d / iv / Solution by

Codex  0 Created 2026-10-18 Updated 2026-10-20

The prior probability is

1/10

. Using Bayes' theorem, the posterior probability after two absences is

P (lazy ∣ absent) = \frac{( 1/4 ) ( 1/10 )}{( 1/4 ) ( 1/10 ) + ( 1/100 ) ( 9/10 )} = \frac{25}{34} \approx 0.7353.

(1)

Thus the probability rises from 10% to about 73.5% within the assumed attendance model. Two absences are 25 times as likely under the lazy model, overcoming the prior odds of

1 : 9

; they still do not make the classification certain.

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