When I was reading about probabilities long time ago, I've written these notes as a tool to simplify multi-events interactions via visualizing them. I hope you find them helpful.

\documentclass{article}
\usepackage{tikz}
\usepackage{geometry}
\geometry{ a4paper,total={170mm,257mm},left=20mm,top=20mm}
\begin{document}
% Definition of circles
\def\firstcircle{ (0.0, 0.0) circle (1.5)}
\def\secondcircle{(2.0, 0.0) circle (1.5)}
\def\thirdcircle{ (1.0,-1.5) circle (1.5)}
\def\rectangle{ (-1.5,-3.0) rectangle (3.5,1.0) }
\colorlet{circle edge}{black}
\colorlet{circle area}{blue!30}
\tikzset{filled/.style={fill=circle area, draw=circle edge, thick},
outline/.style={draw=circle edge, thick}}
\setlength{\parskip}{5mm}
%############################################################################
%############################################################################
%############################################################################
\noindent
\begin{tikzpicture}
\begin{scope}
\clip \firstcircle;
\clip \secondcircle;
\fill[filled] \thirdcircle ;
\end{scope}
\draw[outline] \firstcircle node[left] {$A$};
\draw[outline] \secondcircle node[right] {$B$};
\draw[outline] \thirdcircle node[below] {$C$};
\node[anchor=south] at (current bounding box.north) {$A \cap B \cap C$};
\end{tikzpicture} \qquad
%############################################################################
%############################################################################
%############################################################################
\begin{tikzpicture}
\begin{scope}
\clip \firstcircle \secondcircle \thirdcircle;
\fill[filled] \firstcircle \secondcircle \thirdcircle;
\end{scope}
\draw[outline] \firstcircle node[left] {$A$};
\draw[outline] \secondcircle node[right] {$B$};
\draw[outline] \thirdcircle node[below] {$C$};
\node[anchor=south] at (current bounding box.north) {$A \cup B \cup C$};
\end{tikzpicture} \qquad
%############################################################################
%############################################################################
%############################################################################
\begin{tikzpicture}
\begin{scope}
\clip \firstcircle;
\fill[filled] \secondcircle;
\end{scope}
\draw[outline] \firstcircle node[left] {$A$};
\draw[outline] \secondcircle node[right] {$B$};
\draw[outline] \thirdcircle node[below] {$C$};
\node[anchor=south,align=center] at (current bounding box.north)
{$(A\cap B)=$\\$(A \cap B \cap C) + (A \cap B \cap C')$};
\end{tikzpicture} \\[1.5cm]
%############################################################################
%############################################################################
%############################################################################
\begin{tikzpicture}
\begin{scope}
\clip \firstcircle;
\fill[filled] \thirdcircle;
\end{scope}
\begin{scope}
\clip \firstcircle;
\clip \secondcircle;
\fill[white] \thirdcircle;
\end{scope}
\draw[outline] \firstcircle node[left] {$A$};
\draw[outline] \secondcircle node[right] {$B$};
\draw[outline] \thirdcircle node[below] {$C$};
\node[anchor=south] at (current bounding box.north)
{$(A\cap B' \cap C)$};
\end{tikzpicture} \qquad
%############################################################################
%############################################################################
%############################################################################
\begin{tikzpicture}
\begin{scope}
\fill[filled] \thirdcircle;
\fill[white] \firstcircle;
\fill[white] \secondcircle;
\end{scope}
\draw[outline] \firstcircle node[left] {$A$};
\draw[outline] \secondcircle node[right] {$B$};
\draw[outline] \thirdcircle node[below] {$C$};
\node[anchor=south] at (current bounding box.north)
{$(A' \cap B' \cap C)$};
\end{tikzpicture} \qquad
%############################################################################
%############################################################################
%############################################################################
\begin{tikzpicture}
\begin{scope}
\clip \secondcircle;
\fill[filled] \thirdcircle;
\end{scope}
\fill[filled] \firstcircle;
\draw[outline] \firstcircle node[left] {$A$};
\draw[outline] \secondcircle node[right] {$B$};
\draw[outline] \thirdcircle node[below] {$C$};
\node[anchor=south] at (current bounding box.north)
{$A \cup (B \cap C)$};
\end{tikzpicture} \\[1.5cm]
%############################################################################
%############################################################################
%############################################################################
\begin{tikzpicture}
\begin{scope}
\clip \firstcircle \secondcircle;
\fill[filled] \thirdcircle;
\end{scope}
\draw[outline] \firstcircle node[left] {$A$};
\draw[outline] \secondcircle node[right] {$B$};
\draw[outline] \thirdcircle node[below] {$C$};
\node[anchor=south] at (current bounding box.north)
{$(A \cup B) \cap C$};
\end{tikzpicture} \qquad
\end{document}
\path (a)--(b) node [midway] {text};or using the calc tikzlibrary. (Sorry I can't answer I'm on atablet) – marsupilam Aug 07 '17 at 00:14[pos=.667]between(c)and that midway node(ab). – marsupilam Aug 07 '17 at 00:21