For　a　hypergeometric　distribution,　denoted　by　Hyper(M,　N,　n),　where　N　is　the　population　size,　M　is　the　number　of　population　units　with　some　attribute,　and　n　is　the　given　sample　size,　there　are　two　parametric　cases:　(i)　N　is　unknown　and　M　is　given;　(ii)　M　is　unknown　and　N　is　given.　For　each　case,　we　first　show　that　the　minimum　coverage　probability　of　commonly　used　approximate　intervals　is　much　smaller　than　the　nominal　level　for　any　n,　then　we　provide　exact　smallest　lower　and　upper　one-sided　confidence　intervals　and　an　exact　admissible　two-sided　confidence　interval,　a　complete　set　of　solutions,　for　each　parameter.　Supplementary　materials　for　this　article　are　available　online.