# Example: Tree of probabilities - flipping a coin

Published 2014-07-30 | Author: cis

In mathematics, specifically in statistics, coin-flipping is an introductory example of the complexities of probability and statistics.

This example was written by cis on TikZ.de.

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% Flipping a coin
% Author: cis
\documentclass[border=10pt,varwidth]{standalone}
\usepackage{tikz}
\usetikzlibrary{calc, shapes, backgrounds}
\usepackage{amsmath, amssymb}
\pagecolor{olive!50!yellow!50!white}
\begin{document}
\tikzset{
label = center:\textsf{\Large H}},
tail/.style = {fill = blue!70!yellow, text = black,
label = center:\textsf{\Large T}}
}
\begin{tikzpicture}[
scale = 1.5, transform shape, thick,
every node/.style = {draw, circle, minimum size = 10mm},
grow = down,  % alignment of characters
level 1/.style = {sibling distance=3cm},
level 2/.style = {sibling distance=4cm},
level 3/.style = {sibling distance=2cm},
level distance = 1.25cm
]
\node[fill = gray!40, shape = rectangle, rounded corners,
minimum width = 6cm, font = \sffamily] {Coin flipping}
child { node[shape = circle split, draw, line width = 1pt,
minimum size = 10mm, inner sep = 0mm, font = \sffamily\large,
rotate=30] (Start)
{ \rotatebox{-30}{H} \nodepart{lower} \rotatebox{-30}{T}}
child {   node [head] (A) {}
child { node [head] (B) {}}
child { node [tail] (C) {}}
}
child {   node [tail] (D) {}
child { node [head] (E) {}}
child { node [tail] (F) {}}
}
};

% Filling the root (Start)
\begin{scope}[on background layer, rotate=30]
\fill[head] (Start.base) ([xshift = 0mm]Start.east) arc (0:180:5mm)
-- cycle;
\fill[tail] (Start.base) ([xshift = 0pt]Start.west) arc (180:360:5mm)
-- cycle;
\end{scope}

% Labels
\begin{scope}[nodes = {draw = none}]
\path (Start) -- (A) node [near start, left]  {$0.5$};
\path (A)     -- (B) node [near start, left]  {$0.5$};
\path (A)     -- (C) node [near start, right] {$0.5$};
\path (Start) -- (D) node [near start, right] {$0.5$};
\path (D)     -- (E) node [near start, left]  {$0.5$};
\path (D)     -- (F) node [near start, right] {$0.5$};
\begin{scope}[nodes = {below = 11pt}]
\node [name = X] at (B) {$0.25$};
\node            at (C) {$0.25$};
\node [name = Y] at (E) {$0.25$};
\node            at (F) {$0.25$};
\end{scope}
\draw[densely dashed, rounded corners, thin]
(X.south west) rectangle (Y.north east);
\end{scope}
\end{tikzpicture}
\end{document} 