Let $P = (\{ 0 ,1 \}, \mathcal{F}, \mathbb{P})$ be the D5511: Standard single boolean trial probability space.
Then
| (1) | \begin{equation} \{ 0 \}, \{ 1 \} \in \mathcal{F} \end{equation} |
| (2) | \begin{equation} \{ 0 \} \cap \{ 1 \} = \emptyset \end{equation} |
| (3) | \begin{equation} \mathbb{P}(\{ 0 \} \cap \{ 1 \}) = \mathbb{P}(\emptyset) = 0 \neq \frac{1}{4} = \frac{1}{2} \cdot \frac{1}{2} = \mathbb{P} \{ 0 \} \mathbb{P} \{ 1 \} \end{equation} |