How to set a variable to a random value with bash

One easy method is to use $RANDOM to retrieve a pseudorandom 16 bit integer number in the range [0; 32767]. You can simply convert that to [0; 1] by calculating modulo 2 of the random number:

echo $(( $RANDOM % 2 ))

More information about Bash's $RANDOM: http://www.tldp.org/LDP/abs/html/randomvar.html

With that simple construct you can easily build powerful scripts using randomness, like in this comic...

You could use shuf

DESCRIPTION
     Write a random permutation of the input lines to standard output.

     -i, --input-range=LO-HI
            treat each number LO through HI as an input line
     -n, --head-count=COUNT
            output at most COUNT lines

Example:

$ foo=$(shuf -i0-1 -n1)
$ echo $foo
1
$ foo=$(shuf -i0-1 -n1)
$ echo $foo
0
$ foo=$(shuf -i0-1 -n1)
$ echo $foo
0
$ foo=$(shuf -i0-1 -n1)
$ echo $foo
1

How about:

#!/bin/bash
r=$(($RANDOM % 2))
echo $r

Or even:

r=$(($(od -An -N1 -i /dev/random) % 2))

Or perhaps:

r=$(seq 0 1 | sort -R  | head -n 1)

Or more hackily:

r=$(($(head -128 /dev/urandom | cksum | cut -c1-10) % 2))

And also:

r=$(apg -a 1 -M n -n 1 -m 8 -E 23456789  | cut -c1)

As well as:

r=$((0x$(cut -c1-1 /proc/sys/kernel/random/uuid) % 2))