Firefox on windows 64 bit : use the 32 bit plugins

When installing the java plugin on windows 64 bit (I have windows 7), which Java plugin do I need?
64 bit seems the logical choice.
Here's what Oracle, steward of Java says at this time:

Java for 64-bit browsers

Users should download 64-bit Java software, if they are running 64-bit browsers.

Allright, now do I have a 64 bit firefox, the page tells me how to check

Verify if you are using 32-bit or 64-bit browser

Firefox

To determine whether you are running on a 64-bit version of Firefox, use either of these methods.

• Check the About Firefox panel
• Type in the browser address about:support

If you are running 64-bit Firefox, it may be indicated as 64-bit (e.g., Win64); otherwise it is a 32-bit version of Firefox.  

 What can I find on this page?

 User Agent     Mozilla/5.0 (Windows NT 6.1; WOW64; rv:24.0) Gecko/20100101 Firefox/24.0

There's a number 64 in there, but take care: this indicates that windows is 64 bit. To really know more about your firefox you need to follow the about:buildconfig link. oracle should recommend to type that one directly. Look at the target entry:

target i686-pc-mingw32

This is a 32 bit build after all. As a matter of fact, Firefox does currrently not provides a production quality 64 bit build for Windows. On Windows, Firefox currently is a 32 bit application, hence you always take the 32 bit plugins.