[CentOS] Confusion about 32 vs 64 bit jre

I ran a yum update yesterday and got the new kernel and other goodies, and I've rebooted and all seems to be well.

Except, I just tried to run Firefox for the first time, and it wants a new jre (6.16). Now that's fine, except that I have a recollection of needing the 32-bit jre the last time I did this, but that's not working. I'm pulling down the 64-bit version, but I'm wondering if I need both, which, IIRC, does not work, or which one of the two?

(I _am_ running the x86_64 OS and most apps.)

What bothers me is that I've tried both, and apparently neither one works (!!!!).

I installed by downloading the bin file (self-extracting rpm), and then running the bin with sudo.

Where did I go wrong?

mhr