Drawing Graph of Markov Chain with “Patches” using Tikz

First time using Tikz. Haven't found any documentation on drawing graphs like these, so I have been reading other examples and trying to modify their code to fit my example.

I am trying to reproduce something like this Markov Chain (please excuse my very crude drawing!):

with edges labeled with probabilities which I've tried to incorporate into my code below:

\documentclass[letter,10pt]
\usepackage{amsmath}
\usepackage{tikz}
\usetikzlibrary{automata}
\begin{document}

\begin{center}
\begin{tikzpicture}[->,>=stealth',auto,semithick,node distance=3cm]
\tikzstyle{every state}=[fill=white,draw=black,thick,text=black,scale=1]
\node[state]    (A)                     {$A$};
\node[state]    (B)[above right of=A]   {$B$};
\node[state]    (C)[below right of=A]   {$C$};
\node[state]    (D)[below right of=B]   {$D$};
\path
(A) edge[loop left]     node{$p^2$}         (A);
edge[bend left]     node{$(1-p)^2$}     (B);
edge                node{$p(1-p)$}      (D);
edge[bend right]    node{$p(1-p)$}      (C);
(B) edge                node{$1$}           (D);
(C) edge                node{$1$}           (D);
(D) edge[loop right]    node{$(1-q)^2$}     (D);
edge[bend right]    node{$q(1-q)$}      (B);
edge[bend left]     node{$q(1-q)$}      (C);
edge                node{$q^2$}         (A);
\end{tikzpicture}
\end{center}


Even though I think my structure is correct, most of the paths don't show up and the labels are jumbled and unreadable. If it's also possible, I'd like to group together states $B$, $C$ and $D$ as a patch called $H$, and call state $A$ patch $G$.

Thank you very much for your help!

-

This is an attempt. Only one ; is needed at the end of \path command. Also an oval is added to circle the Patch H and the single line between (A) and (D) is changed to depict lines in the crude image.

Code

\documentclass[letter,10pt]{article}
\usepackage{amsmath}
\usepackage{tikz}
\usetikzlibrary{automata,arrows,positioning,calc}
\begin{document}

\begin{center}
\begin{tikzpicture}[->, >=stealth', auto, semithick, node distance=3cm]
\tikzstyle{every state}=[fill=white,draw=black,thick,text=black,scale=1]
\node[state]    (A)                     {$A$};
\node[state]    (B)[above right of=A]   {$B$};
\node[state]    (C)[below right of=A]   {$C$};
\node[state]    (D)[below right of=B]   {$D$};
\path
(A) edge[loop left]     node{$p^2$}         (A)
edge[bend left]     node{$(1-p)^2$}     (B)
edge[bend left,below]      node{$p(1-p)$}      (D)
edge[bend right]    node{$p(1-p)$}      (C)
(B) edge                node{$1$}           (D)
(C) edge                node{$1$}           (D)
(D) edge[loop right]    node{$(1-q)^2$}     (D)
edge[bend right,right]    node{$q(1-q)$}      (B)
edge[bend left]     node{$q(1-q)$}      (C)
edge[bend left,above]     node{$q^2$}         (A);
\node[above=0.5cm] (A){Patch G};
\draw[red] ($(D)+(-1.5,0)$) ellipse (2cm and 3.5cm)node[yshift=3cm]{Patch H};
\end{tikzpicture}
\end{center}
\end{document}

-
Thank you so much! I didn't know what the semicolons did. That must be why none of my edges showed up. Thank you so much for your time! – EthanAlvaree Jul 29 '14 at 5:18
You are welcome. Indeed, keep in mind, only the last ; is required. – Jesse Jul 29 '14 at 5:20
Also, if you don't want to "hardcode" the position and dimensions of the ellipse, you can \usetikzlibrary{fit} and: \node[draw=red,ellipse, inner sep=0pt, fit=(B) (C) (D)] (patch) {}; \node[below=5mm of patch.north, red] {Patch H}; – JLDiaz Jul 29 '14 at 8:20
Thanks @JLDiaz, did think of that. But thinking that mine was quicker/easier, IMHO. – Jesse Jul 29 '14 at 8:30
A very great example which helped me a lot! Thank you for posting this! – math12 Oct 13 '14 at 17:35