[Tex/LaTex] Probability tree is colliding

diagramstikz-treestrees

I need to make a probability tree with 3 outcomes per event. Here is the code I am using:

\documentclass{article}
\usepackage[utf8]{inputenc}
\usepackage{fullpage}
\usepackage{amsmath}
\usepackage{tikz}
\usetikzlibrary{trees}

\begin{document}

% Set the overall layout of the tree
\tikzstyle{level 1}=[level distance=3.5cm, sibling distance=3.5cm]
\tikzstyle{level 2}=[level distance=3.5cm, sibling distance=2cm]

% Define styles for bags and leafs
\tikzstyle{bag} = [text width=4em, text centered]
\tikzstyle{end} = [circle, minimum width=3pt,fill, inner sep=0pt]

\begin{tikzpicture}[grow=right, sloped]
\node[bag] {Urn $3G, 4R, 2W$}
    child {
        node[bag] {$2G, 4R, 2W$}        
            child {
                node[end, label=right: {$P(G_1\cap G_2)=\frac{1}{3}\times\frac{1}{4}=\frac{1}{12}$}] {}
                edge from parent
                node[above] {$G$}
                node[below]  {$\frac{1}{4}$}
            }
            child {
                node[end, label=right: {$P(G_1\cap R_2)=\frac{1}{3}\times\frac{1}{2}=\frac{1}{6}$}] {}
                edge from parent
                node[above] {$R$}
                node[below]  {$\frac{1}{2}$}
            }
            child {
                node[end, label=right: {$P(G_1\cap W_2)=\frac{1}{3}\times\frac{1}{4}=\frac{1}{12}$}] {}
                edge from parent
                node[above] {$W$}
                node[below]  {$\frac{1}{4}$}
            }
            edge from parent 
            node[above] {$G$}
            node[below]  {$\frac{1}{3}$}
    }
    child {
        node[bag] {$3G, 3R, 2W$}   
            child {
                node[end, label=right: {$P(R_1\cap G_2)=\frac{4}{9}\times\frac{3}{8}=\frac{2}{5}$}] {}
                edge from parent
                node[above] {$G$}
                node[below]  {$\frac{3}{8}$}
            }
            child {
                node[end, label=right: {$P(R_1\cap R_2)=\frac{4}{9}\times\frac{3}{8}=\frac{4}{15}$}] {}
                edge from parent
                node[above] {$R$}
                node[below]  {$\frac{3}{8}$}
            }
            child {
                node[end, label=right: {$P(R_1\cap W_2)=\frac{4}{9}\times\frac{1}{4}=\frac{4}{15}$}] {}
                edge from parent
                node[above] {$W$}
                node[below]  {$\frac{1}{4}$}
            }
            edge from parent 
            node[above] {$R$}
            node[below]  {$\frac{4}{9}$}
    }
    child {
        node[bag] {$3G, 4R, 1W$}   
            child {
                node[end, label=right: {$P(W_1\cap G_2)=\frac{2}{9}\times\frac{3}{8}=\frac{1}{12}$}] {}
                edge from parent
                node[above] {$G$}
                node[below]  {$\frac{3}{8}$}
            }
            child {
                node[end, label=right: {$P(W_1\cap R_2)=\frac{2}{9}\times\frac{1}{2}=\frac{1}{9}$}] {}
                edge from parent
                node[above] {$R$}
                node[below]  {$\frac{1}{2}$}
            }
            child {
                node[end, label=right: {$P(W_1\cap W_2)=\frac{2}{9}\times\frac{1}{8}=\frac{1}{36}$}] {}
                edge from parent
                node[above] {$W$}
                node[below]  {$\frac{1}{8}$}
            }
            edge from parent         
            node[above] {$W$}
            node[below]  {$\frac{2}{9}$}
    };
\end{tikzpicture}

\end{document}

Which produces

How can I make this tree less "squeezed"?

I would rather not use an alternative, I've been using this same tree for other situations with just 2 outcomes per event.

Best Answer

Basically, with this approach to drawing trees, you have to figure out suitable spacing for the tree. TikZ doesn't do it for you.

In this case, the bag nodes need to be wider (or you need to break the lines when mathematical expressions are too long). To avoid the crossings of edges and mixing up of nodes, you need to increase the sibling distance for level 1 relative to the sibling distance for level 2.

For example:

\documentclass[tikz,border=10pt,multi]{standalone}
\usetikzlibrary{trees}
\begin{document}
\tikzset{%
  level 1/.style={level distance=3.5cm, sibling distance=4.5cm},
  level 2/.style={level distance=3.5cm, sibling distance=2cm},
  bag/.style={text width=50pt, text centered},
  end/.style={circle, minimum width=3pt, fill, inner sep=0pt},
}
\begin{tikzpicture}[grow=right, sloped]
  \node[bag] {Urn $3G, 4R, 2W$}
  child {
    node[bag] {$2G, 4R, 2W$}
    child {
      node[end, label=right: {$P(G_1\cap G_2)=\frac{1}{3}\times\frac{1}{4}=\frac{1}{12}$}] {}
      edge from parent
      node[above] {$G$}
      node[below]  {$\frac{1}{4}$}
    }
    child {
      node[end, label=right: {$P(G_1\cap R_2)=\frac{1}{3}\times\frac{1}{2}=\frac{1}{6}$}] {}
      edge from parent
      node[above] {$R$}
      node[below]  {$\frac{1}{2}$}
    }
    child {
      node[end, label=right: {$P(G_1\cap W_2)=\frac{1}{3}\times\frac{1}{4}=\frac{1}{12}$}] {}
      edge from parent
      node[above] {$W$}
      node[below]  {$\frac{1}{4}$}
    }
    edge from parent
    node[above] {$G$}
    node[below]  {$\frac{1}{3}$}
  }
  child {
    node[bag] {$3G, 3R, 2W$}
    child {
      node[end, label=right: {$P(R_1\cap G_2)=\frac{4}{9}\times\frac{3}{8}=\frac{2}{5}$}] {}
      edge from parent
      node[above] {$G$}
      node[below]  {$\frac{3}{8}$}
    }
    child {
      node[end, label=right: {$P(R_1\cap R_2)=\frac{4}{9}\times\frac{3}{8}=\frac{4}{15}$}] {}
      edge from parent
      node[above] {$R$}
      node[below]  {$\frac{3}{8}$}
    }
    child {
      node[end, label=right: {$P(R_1\cap W_2)=\frac{4}{9}\times\frac{1}{4}=\frac{4}{15}$}] {}
      edge from parent
      node[above] {$W$}
      node[below]  {$\frac{1}{4}$}
    }
    edge from parent
    node[above] {$R$}
    node[below]  {$\frac{4}{9}$}
  }
  child {
    node[bag] {$3G, 4R, 1W$}
    child {
      node[end, label=right: {$P(W_1\cap G_2)=\frac{2}{9}\times\frac{3}{8}=\frac{1}{12}$}] {}
      edge from parent
      node[above] {$G$}
      node[below]  {$\frac{3}{8}$}
    }
    child {
      node[end, label=right: {$P(W_1\cap R_2)=\frac{2}{9}\times\frac{1}{2}=\frac{1}{9}$}] {}
      edge from parent
      node[above] {$R$}
      node[below]  {$\frac{1}{2}$}
    }
    child {
      node[end, label=right: {$P(W_1\cap W_2)=\frac{2}{9}\times\frac{1}{8}=\frac{1}{36}$}] {}
      edge from parent
      node[above] {$W$}
      node[below]  {$\frac{1}{8}$}
    }
    edge from parent
    node[above] {$W$}
    node[below]  {$\frac{2}{9}$}
  };
\end{tikzpicture}
\end{document}

Despite your saying you're not interested in alternative solutions, I cannot draw a tree without offering a Forest solution. Well, not usually.

The nice think about Forest is that the tree can be specified very concisely. Although I've not done so here, it would not be difficult to create the content of the final layer of nodes programmatically by collecting the labels above and below the edges.

The style probability tree can be reused once defined. When used, it allows you to say my label=<above>:<below> to specify the edge labels. The final tier's labels are specified within the nodes (or could be automated, as mentioned above) and the circles are created using a suitable 'arrow' for the edge. s sep and l sep are used to ensure the tree is spread out sufficiently to accommodate the edge labels (because Forest can do this bit automatically), but no measures are needed to ensure that the tree's main nodes and edges do not conflict (Forest does do this automatically).

\documentclass[tikz,border=10pt,multi]{standalone}
\usetikzlibrary{arrows.meta}
\usepackage{forest}
\begin{document}
\forestset{%
  declare toks={my label}{},
  probability tree/.style={%
    for tree={%
      math content,
      grow'=0,
      child anchor=parent,
      l sep+=40pt,
      +edge={every node/.append style={sloped, midway}},
      delay={%
        split option={my label}{:}{above edge, below edge},
      }
    },
    where n children=0{%
      +edge={-{Circle[width=3pt,length=3pt]}},
      if n=1{
        !u.s sep+=20pt,
      }{}
    }{%
      text width=50pt,
      text centered,
      if={isodd(n_children)}{%
        for n/.wrap pgfmath arg={{##1}{calign with current edge}}{int(.5*(n_children()+1))}
      }{},
    },
    above edge/.style={%
      +edge label={node [above] {$##1$}},
    },
    below edge/.style={%
      +edge label={node [below] {$##1$}},
    },
  },
}
\begin{forest}
  probability tree
  [{Urn $3G, 4R, 2W$}, plain content
  [{2G, 4R, 2W}, my label=G:\frac{1}{3}
      [{P(G_1\cap G_2)=\frac{1}{3}\times\frac{1}{4}=\frac{1}{12}}, my label=G:\frac{1}{4}
      ]
      [{P(G_1\cap R_2)=\frac{1}{3}\times\frac{1}{2}=\frac{1}{6}},my label=R:\frac{1}{2}
      ]
      [{P(G_1\cap W_2)=\frac{1}{3}\times\frac{1}{4}=\frac{1}{12}},my label=W:\frac{1}{4}
      ]
    ]
    [{3G, 3R, 2W}, my label=R:\frac{4}{9}
      [{P(R_1\cap G_2)=\frac{4}{9}\times\frac{3}{8}=\frac{2}{5}},my label=G:\frac{3}{8}
      ]
      [{P(R_1\cap R_2)=\frac{4}{9}\times\frac{3}{8}=\frac{4}{15}},my label=R:\frac{3}{8}
      ]
      [{P(R_1\cap W_2)=\frac{4}{9}\times\frac{1}{4}=\frac{4}{15}}, my label=W:\frac{1}{4}
      ]
    ]
    [{3G, 4R, 1W}, my label=W:\frac{2}{9}
      [{P(W_1\cap G_2)=\frac{2}{9}\times\frac{3}{8}=\frac{1}{12}},my label=G:\frac{3}{8}
      ]
      [{P(W_1\cap R_2)=\frac{2}{9}\times\frac{1}{2}=\frac{1}{9}},my label=R:\frac{1}{2}
      ]
      [{P(W_1\cap W_2)=\frac{2}{9}\times\frac{1}{8}=\frac{1}{36}},my label=W:\frac{1}{8}
      ]
    ]
  ]
\end{forest}
\end{document}

Related Solutions

[Tex/LaTex] Probability tree using TikZ for Bernoulli experiments

I work on something like that but I need to work on this code (no time actually) You can look at \pgfqkeys{/berntree} to see all the options. The limit is 5 but it would be nice to use a recurrent method to build this tree ! I made some modifications now you can modify the styles : node success stylean node miss style. To add some labels at the end of each branch , you can use the last nodes ( it's not very easy) and for the label on the edges you can use edge style. The code is not very fine because the arrows are inside some nodes and it would be better to give the same size for each nodes. Version 4 : edge style/.style = {->,>=latex',shorten <= 6pt}for the edge's problem and see the final loops for the labels. I fixed the size's nodes

\documentclass{scrartcl}
\usepackage{pgf,tikz} 
\usetikzlibrary{trees,arrows,calc} 

\makeatletter
\newcount\tkz@Berndepth
\newdimen\tkz@BernLEN
\tkz@BernLEN=24em 
\def\tkzBernTreeSet#{\pgfqkeys{/berntree}} 

\pgfqkeys{/berntree}{%
  success/.code      = \def\tkz@bern@success{#1},
  miss/.code         = \def\tkz@bern@miss{#1},
  p/.code            = \def\tkz@bern@pbsuccess{#1},
  q/.code            = \def\tkz@bern@pbmiss{#1},
  node success style/.style  = {inner sep=2pt,outer sep=3pt},
  node miss style/.style  = {inner sep=2pt,outer sep=3pt},
  edge style/.style  = {->,>=latex',shorten <= 6pt},
  root style/.style  = {draw,circle},
  success/.initial   = S,
  miss/.initial      = E, 
  p/.initial         = $p$,
  q/.initial         = $1-p$,
  gap/.code          = \def\tkz@bern@gap{#1},
  length/.code       = \def\tkz@bern@length{#1} 
} 

\def\tkz@brntree#1#2{%
  \node[/berntree/root style] {};
\global\advance\tkz@Berndepth 1\relax
\begin{scope}[level distance=\tkz@bern@length,
              level 1/.style={sibling distance=#2}]   
  \node[] (root) at (#1) {}     
  [grow=right]
  child[/berntree/edge style] {%
    node[/berntree/node miss style](tkz@E\the\tkz@Berndepth) {\tkz@bern@miss} 
            edge from parent node[fill=white] {\tkz@bern@pbmiss}}
  child [/berntree/edge style] {%
    node[/berntree/node success style] (tkz@S\the\tkz@Berndepth) {\tkz@bern@success} 
            edge from parent node[fill=white] {\tkz@bern@pbsuccess}
             };
\end{scope}}% 

\def\tkzBernTree{\pgfutil@ifnextchar[{\tkz@BernTree}{\tkz@BernTree[]}}
\def\tkz@BernTree[#1]#2{%
\begingroup  
\pgfqkeys{/berntree}{%
success = S,
miss= E,
node success style/.style  = {inner sep=2pt,outer sep=3pt,draw,minimum width=1.5em,minimum height=1.5em},
node miss style/.style  = {inner sep=2pt,outer sep=3pt,circle,draw,minimum width=1.5em},
p=$p$,
q=$q$,
gap=8cm,
length=3cm} 
\pgfqkeys{/berntree}{#1}
  \tkz@BernLEN=\tkz@bern@gap\relax    
  \tkz@Berndepth 0\relax 
  \node (tkz@S0) at (0,0){}; 
\def\tkz@bn@level{#2} 
 \ifcase\tkz@bn@level%
 \or% 
  \tkz@brntree{tkz@S0}{\tkz@BernLEN} 
 \or% 
   \tkz@brntree{tkz@S0}{\tkz@BernLEN} 
  \divide \tkz@BernLEN by 2 %
 \foreach \nd in {1}{   
   \tkz@brntree{tkz@S\nd}{\tkz@BernLEN}
   \tkz@brntree{tkz@E\nd}{\tkz@BernLEN}}
 \or%
   \tkz@brntree{tkz@S0}{\tkz@BernLEN}  
   \divide \tkz@BernLEN by 2 %
 \foreach \nd in {1}{   
   \tkz@brntree{tkz@S\nd}{\tkz@BernLEN}
   \tkz@brntree{tkz@E\nd}{\tkz@BernLEN}}   
  \divide \tkz@BernLEN by 2 %
 \foreach \nd in {2,3}{   
   \tkz@brntree{tkz@S\nd}{\tkz@BernLEN}
   \tkz@brntree{tkz@E\nd}{\tkz@BernLEN}} 
 \or% 
   \tkz@brntree{tkz@S0}{\tkz@BernLEN}  
   \divide \tkz@BernLEN by 2 %
 \foreach \nd in {1}{   
   \tkz@brntree{tkz@S\nd}{\tkz@BernLEN}
   \tkz@brntree{tkz@E\nd}{\tkz@BernLEN}}   
  \divide \tkz@BernLEN by 2 %
 \foreach \nd in {2,3}{   
   \tkz@brntree{tkz@S\nd}{\tkz@BernLEN}
   \tkz@brntree{tkz@E\nd}{\tkz@BernLEN}} 
  \divide \tkz@BernLEN by 2 %
 \foreach \nd in {4,5,6,7}{   
   \tkz@brntree{tkz@S\nd}{\tkz@BernLEN}
   \tkz@brntree{tkz@E\nd}{\tkz@BernLEN}}    
  \or% 
   \tkz@brntree{tkz@S0}{\tkz@BernLEN}  
   \divide \tkz@BernLEN by 2 %
 \foreach \nd in {1}{   
   \tkz@brntree{tkz@S\nd}{\tkz@BernLEN}
   \tkz@brntree{tkz@E\nd}{\tkz@BernLEN}}   
  \divide \tkz@BernLEN by 2 %
 \foreach \nd in {2,3}{   
   \tkz@brntree{tkz@S\nd}{\tkz@BernLEN}
   \tkz@brntree{tkz@E\nd}{\tkz@BernLEN}} 
  \divide \tkz@BernLEN by 2 %
 \foreach \nd in {4,...,7}{   
   \tkz@brntree{tkz@S\nd}{\tkz@BernLEN}
   \tkz@brntree{tkz@E\nd}{\tkz@BernLEN}} 
   \divide \tkz@BernLEN by 2 %
 \foreach \nd in {8,...,15}{   
   \tkz@brntree{tkz@S\nd}{\tkz@BernLEN}
   \tkz@brntree{tkz@E\nd}{\tkz@BernLEN}}   
 \fi   
 \endgroup
 }
\makeatother
\begin{document}

 \begin{tikzpicture}[yscale=1.2]
\tkzBernTree[root style/.style  = {fill,circle,outer sep =1pt,inner sep=2pt}]{4}
\makeatletter 
 \foreach \num/\lab in {8/a,9/c,10/e,11/g,12/i,13/k,14/m,15/o}{%
 \node at ($(tkz@S\num)+(2,0)$){$\lab$};
 } 
  \foreach \num/\lab in {8/b,9/d,10/f,11/h,12/j,13/l,14/n,15/p}{%
 \node at ($(tkz@E\num)+(2,0)$){$\lab$};
 }  
\makeatother  
 \end{tikzpicture} 

\end{document}

enter image description here

[Tex/LaTex] Tikz-Tree: Arrow-style depending on parent node

You can set an option that only applies to the children, if you use the every child style.

The no edge from this parent style is setup in a way that the children of the child it is used on doesn’t draw the edge.

Instead of draw one you can set any other option an edge can have. This does not include a \draw command!

For edges in a tree there is a special key that sets the path: edge from parent path.

The default path is

(\tikzparentnode\tikzparentanchor) -- (\tikzchildnode\tikzchildanchor)

Code

\documentclass[tikz,convert=false]{standalone}
\begin{document}
\begin{tikzpicture}[
  no edge from this parent/.style={
    every child/.append style={
      edge from parent/.style={draw=none}}},
  a/.style={circle, draw=black},
  b/.style={rectangle, draw=red},
]
\node[a] {}
  child {node[a] {}}
  child[no edge from this parent] {node[b] {no}
    child {node[a] {no}}
    child {node[b] {no}}
  }
  child {node[a] {}}
;
\end{tikzpicture}
\end{document}

Output