Let two natural integers $A$ and $n$ such that $n \leqslant A$ and $p$ a real number between 0 and 1. We assume $pA \in \mathbb{N}$ and we denote $q = 1-p$. Let $X$ be a discrete real random variable. We say that $X$ follows the hypergeometric distribution with parameters $n, p$ and $A$ when $$\left\{\begin{array}{l} X(\Omega) \subset \llbracket 0, n \rrbracket, \\ \mathbb{P}(X = k) = \frac{\binom{pA}{k}\binom{qA}{n-k}}{\binom{A}{n}} \quad \text{for all } k \in \llbracket 0, n \rrbracket. \end{array}\right.$$ Verify that we have indeed defined a probability distribution.
Let two natural integers $A$ and $n$ such that $n \leqslant A$ and $p$ a real number between 0 and 1. We assume $pA \in \mathbb{N}$ and we denote $q = 1-p$. Let $X$ be a discrete real random variable. We say that $X$ follows the hypergeometric distribution with parameters $n, p$ and $A$ when
$$\left\{\begin{array}{l} X(\Omega) \subset \llbracket 0, n \rrbracket, \\ \mathbb{P}(X = k) = \frac{\binom{pA}{k}\binom{qA}{n-k}}{\binom{A}{n}} \quad \text{for all } k \in \llbracket 0, n \rrbracket. \end{array}\right.$$
Verify that we have indeed defined a probability distribution.