I'm having trouble finding concise information about this. What does the overline in probability and statistics mean?
After looking around for a bit i found out it could be a complement, as in $\overline A\cap B = \text{"Not $A$ and $B$"}$ which I found is usually written as $A'\cap B$ but is sometimes written is many different ways. But if it does mean the same as $'$, then what does the double overline mean?
Examples: $$ \overline{A}\cap B; \qquad \overline{A}\cup B; \qquad \overline{\overline{A}\cap \overline{B}}.$$
The overline here is not being used in the sense of probability and statistics[1], but in the sense of set theory. In set theory, the overline typically denotes the complement of a set. In this context, $$ \overline{\overline{A}\cap\overline{B}}$$ is the complement of the set obtained by taking the intersection of the complements of $A$ and $B$. Expanding things out a little, define the set $$ C = \overline{A}\cap \overline{B}.$$ In words, $C$ is the set of all things which are contained in neither $A$ nor $B$. Then $$ \overline{\overline{A}\cap\overline{B}} = \overline{C} = \{ x : x\not\in C \}.$$ A "prime" is also often used for the set complement, e.g. $A'$, though there is potential that this notation could be confused with the derivative, or with some notion of duality. My own preference is to use $A^\complement$ to denote the complement of a set, as this notation is not (to my knowledge) used anywhere else in mathematics, and so it has very little likelihood of being confusing or ambiguous. With this notation, $$ \overline{\overline{A}\cap\overline{B}} = \left( A^\complement \cap B^\complement \right)^\complement. $$
[1] In statistics, the overline typically denotes the sample mean. That is, if we take a random sample from a population, and measure some statistic (say, $x_n$ is the height of the $n$-th person sampled), then $\overline{x}$ denotes the mean of sampled measurements, i.e. $$ \overline{x} = \frac{x_1 + x_2 + \dotsb + x_n}{n}. $$