Explanation Notation Union Probability Could somebody explain how to create intuition for the probability/union notation below? I don't know how to read it.

And is this a situation where events are disjoint, but dependent?
 A: No, that's not union notation.
I will create some variables to highlight the difference.
Let $N$ be the number of sixes in four rolls. Let $R_i = 0$ if the $i$th roll is not a six, and $R_i = 1$ if it is a six. Notice that the complement of $\{N\geq 1\}$ is $\{N = 0\}$.
Finally notice that
$$\{N =0\}\iff\{R_1=0\text{ and }R_2 = 0\text{ and }R_3 = 0\text{ and }R_ 4= 0\}.$$
Then the question becomes
\begin{align*}
P(R_1 = 1\cup R_2 = 1\cup\dotsb\cup R_4 = 1)
&=P\left(\bigcup_{k = 1}^4R_i = 1\right)\\
&=P(N\geq 1) \\
&= 1-P(N = 0)\\
&=1-P\left(\bigcap_{k = 1}^4R_i = 0\right)\\
&=1-P(R_1 = 0\cap R_2 = 0\cap\dotsb\cap R_4 = 0)\\
&=1-P(R_1 = 0)P(R_2 = 0)\dotsm P(R_4 = 0)\tag1\\
&=1- \left(\frac{5}{6}\right)^4
\end{align*}
where $\cap$ is an intersection, $\cup$ is a union, and $(1)$ is true by independence. In plain words, unions can be read as "or" and intersections can be read as "and".
The big $\displaystyle \bigcap_{k=1}^4$ and big $\displaystyle \bigcup_{k = 1}^4$ notation work like the big $\displaystyle \sum_{k = 1}^4$ notation.
