Set with n items, k of which have a certain property k<=n, m items randomly from that set m<=n, what is the distribution of the number of chosen items having that property?

Paola Mayer

Paola Mayer

Answered question

2022-10-28

Set with n items, k of which have a certain property k n, m items randomly from that set m n, what is the distribution of the number of chosen items having that property? An item can only be chosen once.
expect an answer in the form ( f ( k , n , m ) g ( k , n , m ) ) , but I don't know f ( k , n , m ) and g ( k , n , m ).

Answer & Explanation

garbhaighzf

garbhaighzf

Beginner2022-10-29Added 13 answers

Begin by counting all samples of m elements from the population of n; this can be done ( n m ) ways. Suppose exactly l of the k special items are chosen; let us enumerate the possibilities. There are ( k l ) ways to choose the special items and then ( n k m l ) ways to choose the non-special ones. Now divide; here we assume all samples are equiprobable. We get

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