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

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- Solution ii

Solution

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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