Now, you are not sure if OpenJDK is installed on fedora or not. So you can try to install it. If it is already installed, nothing.
Step 1: We will try to install OpenJDK6 on fedora
If you are root, then do this:
$> yum install java-1.6.0-openjdk
else, if you have sudo rights, then
home $> sudo yum install java-1.6.0-openjdk
Step 2: Where is OpenJDK installed on fedora?
If you do not know the rpm name, try to do step 1 above to install. That will give you the rpm name.
$> sudo rpm -ql java-1.6.0-openjdk-126.96.36.199-34.b17.fc12.x86_64