Basement Bathroom Venting Help
I'm going to venture a guess here (at least until photos come). 2.5" isn't a pipe size so I'm going to go out on a limb and call it 3 inch that will be for your toilet. Regarding the bucket I'm going to guess that only a bottom half of the bucket is showing which means that there is a space in there to put a trap for a shower or tub. If the previous statements are correct then the one and a half inch pipe is really a 2"  which is a wet vent for your sink.

In the floor it would look somewhat like thiswww.doityourself.com