# Probability Tree Diagrams in R

As part of a Problem Solving Course that I teach, I have several sessions on probability theory. Given that attorneys must frequently make decisions in environments of uncertainty, probability can be a useful skill for law students to learn.

Conditional probability, and Bayes’ Theorem, are important sub-topics that I focus upon.  In teaching my students about Conditional Probability, it is often helpful to create a Conditional Probability Tree diagram like the one pictured below (sometimes called a probability tree).  I’ll explain in a future post why such a diagram/graph is a useful visualization for learners.

(See also this Javascript Conditional Probability Tree Diagram webpage that I created in that I describe in a different post.)

## No Probability Tree Diagrams in R ?

Like many others, I use the popular free, and open-source R statistical programming language.  R is one of the top computing platforms in which to perform machine learning and other statistical tasks (along with Python – another favorite of mine).  To program in R, I use the excellent R-Studio application which makes the experience much better.

Given the relationship between R and statistics, I was somewhat surprised that I was unable to find any easily accessible R code or functions to create visually appealing Conditional Probability Tree diagrams like the one above.

Thus, I put together some basic R code below for visualizing conditional probability trees, using the Rgraphviz R package.  You must install the Rgraphviz package before using the R code below. If you know of other ways to create visually appealing conditional probability tree in R that I may have missed in my search, please let me know.

I thought I’d release the code below to others in case it is useful.

(Caveat:  This is rough code, and has not been thoroughly tested, and is just meant as a starting example to help make your own probability tree diagrams – so no guarantees).

(You can also look at this other post about creating a Probability Tree Diagram Using Javascript and D3 if R is not your preferred platform.)

### R Code to Create a Visual Conditional Probability Tree

```
# R Conditional Probability Tree Diagram

# The Rgraphviz graphing package must be installed to do this
require("Rgraphviz")

# Change the three variables below to match your actual values
# These are the values that you can change for your own probability tree
# From these three values, other probabilities (e.g. prob(b)) will be calculated

# Probability of a
a<-.01

# Probability (b | a)
bGivena<-.99

# Probability (b | ¬a)
bGivenNota<-.10

###################### Everything below here will be calculated

# Calculate the rest of the values based upon the 3 variables above
notbGivena<-1-bGivena
notA<-1-a
notbGivenNota<-1-bGivenNota

#Joint Probabilities of a and B, a and notb, nota and b, nota and notb
aANDb<-a*bGivena
aANDnotb<-a*notbGivena
notaANDb <- notA*bGivenNota
notaANDnotb <- notA*notbGivenNota

# Probability of B
b<- aANDb + notaANDb
notB <- 1-b

# Bayes theorum - probabiliyt of A | B
# (a | b) = Prob (a AND b) / prob (b)
aGivenb <- aANDb / b

# These are the labels of the nodes on the graph
# To signify "Not A" - we use A' or A prime

node1<-"P"
node2<-"A"
node3<-"A'"
node4<-"A&B"
node5<-"A&B'"
node6<-"A'&B"
node7<-"A'&B'"
nodeNames<-c(node1,node2,node3,node4, node5,node6, node7)

rEG <- new("graphNEL", nodes=nodeNames, edgemode="directed")
#Erase any existing plots
dev.off()

# Draw the "lines" or "branches" of the probability Tree
rEG <- addEdge(nodeNames[1], nodeNames[2], rEG, 1)
rEG <- addEdge(nodeNames[1], nodeNames[3], rEG, 1)
rEG <- addEdge(nodeNames[2], nodeNames[4], rEG, 1)
rEG <- addEdge(nodeNames[2], nodeNames[5], rEG, 1)
rEG <- addEdge(nodeNames[3], nodeNames[6], rEG, 1)
rEG <- addEdge(nodeNames[3], nodeNames[7], rEG, 10)

eAttrs <- list()

q<-edgeNames(rEG)

# Add the probability values to the the branch lines

eAttrs\$label <- c(toString(a),toString(notA),
toString(bGivena), toString(notbGivena),
toString(bGivenNota), toString(notbGivenNota))
names(eAttrs\$label) <- c(q[1],q[2], q[3], q[4], q[5], q[6])
edgeAttrs<-eAttrs

# Set the color, etc, of the tree
attributes<-list(node=list(label="foo", fillcolor="lightgreen", fontsize="15"),
edge=list(color="red"),graph=list(rankdir="LR"))

#Plot the probability tree using Rgraphvis
plot(rEG, edgeAttrs=eAttrs, attrs=attributes)
nodes(rEG)
edges(rEG)

#Add the probability values to the leaves of A&B, A&B', A'&B, A'&B'
text(500,420,aANDb, cex=.8)

text(500,280,aANDnotb,cex=.8)

text(500,160,notaANDb,cex=.8)

text(500,30,notaANDnotb,cex=.8)

text(340,440,"(B | A)",cex=.8)

text(340,230,"(B | A')",cex=.8)

#Write a table in the lower left of the probablites of A and B
text(80,50,paste("P(A):",a),cex=.9, col="darkgreen")
text(80,20,paste("P(A'):",notA),cex=.9, col="darkgreen")

text(160,50,paste("P(B):",round(b,digits=2)),cex=.9)
text(160,20,paste("P(B'):",round(notB, 2)),cex=.9)

text(80,420,paste("P(A|B): ",round(aGivenb,digits=2)),cex=.9,col="blue")

```

### Harry Surden

Harry Surden is an Professor of Law at the University of Colorado Law School and affiliated faculty at the Stanford Center for Legal Informatics (CodeX). His scholarship centers upon artificial intelligence and law, patents and copyright, information privacy law, legal informatics and legal automation, and the application of computer technology within the legal system. He is a former professional software engineer.

His Twitter is : @Harry Surden