A D5748: Random positive integer $X \in \text{Random} \{ 1, 2, 3, 4, 5, 6 \}$ is the fair die random positive integer if and only if \begin{equation} \mathbb{P}(X = 1) = \mathbb{P}(X = 2) = \cdots = \mathbb{P}(X = 6) = \frac{1}{6} \end{equation}