 Solution

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/a/ii/solution

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

Choose

n

students from the

L

lazy students and

S - n

from the other

N - L

. Dividing by the total number of possible college memberships gives

P (n lazy) = \frac{( n L ) ( S - n N - L )}{( S N )}, 0 \leq n \leq S .

The assumptions ensure all these values are possible. This sampling is without replacement, as required by the hypergeometric distribution.

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