Do I still need to download 32-bit browser plugins for my 64-bit system?

This is probably one of the common (if potentially stupid) questions that's bound to get ask. I'm currently on a 64-bit system (running Windows 7) & when it comes to browser plugins, I'm always wondering if I still need to download the 32-bit versions of Java & Flash to use with my browsers OR do the... show more This is probably one of the common (if potentially stupid) questions that's bound to get ask.

I'm currently on a 64-bit system (running Windows 7) & when it comes to browser plugins, I'm always wondering if I still need to download the 32-bit versions of Java & Flash to use with my browsers OR do the 64-bit versions include the 32-bit counterparts as well?

Right now, I'm downloading both to be on the safe side, but the big question is...

Am what I'm doing necessary (downloading both)?
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