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Hypergeometric distribution
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=== Symmetries === Swapping the roles of green and red marbles: : <math> f(k;N,K,n) = f(n-k;N,N-K,n)</math> Swapping the roles of drawn and not drawn marbles: : <math> f(k;N,K,n) = f(K-k;N,K,N-n)</math> Swapping the roles of green and drawn marbles: : <math> f(k;N,K,n) = f(k;N,n,K) </math> These symmetries generate the [[dihedral group]] <math>D_4</math>.
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