Both /etc/bashrc and ~/.bashrc are whats referred to as non-login files. Meaning they do not get sourced during a login shell unless called by /etc/profile or another file.

If /etc/profile calls it (as is typical) then if you want to test it in your current shell you have to either source it.

/root: #> source .bashrc (source with the command source)

/root: # . .bashrc (source with a period)

Or you have to instantiate a login shell by using su or sudo.

/root: # su - (the dash starts a login shell which will re-source login files)

/root: # sudo su - (using sudo to perform the switch user command)

and of course you could just re-login.

EDIT:

Typically though Java paths are not set using .bashrc they are set as separate scripts in the /etc/profile.d directory. At least on the enterprise distributions I use.

system1:/etc/profile.d # ll
-rw-r--r-- 1 root root  1438 Aug 30  2005 alljava.csh
-rw-r--r-- 1 root root  1682 Jul 13  2005 alljava.sh

system1:/etc/profile.d # cat alljava.sh
if [ -x /usr/$__libdir/jvm/java/bin/java ] || [ -x /usr/$__libdir/jvm/java/bin/jre ] ; then
export JAVA_BINDIR=/usr/$__libdir/jvm/java/bin
export JAVA_ROOT=/usr/$__libdir/jvm/java
export JAVA_HOME=/usr/$__libdir/jvm/java
#....cut for brevity...

First, you have a typo in export line. It should be

export PATH=$PATH:$JAVA_HOME/bin

No space, add a $ character before JAVA_HOME, add /bin

However fixing above line may not fix your problem in installing java. The easiest way to install java is by using webup8 ppa:

sudo add-apt-repository ppa:webupd8team/java
sudo apt-get update
sudo apt-get install oracle-java7-installer

After the last command, the script will automatically download the jdk from Oracle website and install it for you. You can read the tutorial here.

You can set your JAVA_HOME in /etc/profile as Petronilla Escarabajo suggests. But the preferred location for JAVA_HOME or any system variable is /etc/environment.

Open /etc/environment in any text editor like nano or gedit and add the following line:

JAVA_HOME="/usr/lib/jvm/open-jdk"

(java path could be different)

Use source to load the variables, by running this command:

source /etc/environment

Then check the variable, by running this command:

echo $JAVA_HOME

Update

Usually most linux systems source /etc/environment by default. If your system doesn't do that add the following line to ~/.bashrc (Thanks @pje)

source /etc/environment

It seems that you do not have a Java JDK (Java Development Kit) installed, if you try run the following command you:

javac -version

probably you will get the following:

The program 'javac' can be found in the following packages:
 * default-jdk
 * ecj
 * gcj-4.6-jdk
 * gcj-4.7-jdk
 * openjdk-7-jdk
 * openjdk-6-jdk
Try: sudo apt-get install <selected package>

So, you have to run the following command will install the OpenJDK version of the Java JDK:

sudo apt-get install default-jdk

1. find /usr/lib/jvm/java-1.x.x-openjdk

2. vim /etc/profile

   Prepend sudo if logged in as not-privileged user, ie. sudo vim

3. Press 'i' to get in insert mode

4. add:

   export JAVA_HOME="path that you found"
   
   export PATH=$JAVA_HOME/bin:$PATH
   

5. logout and login again, reboot, or use source /etc/profile to apply changes immediately in your current shell