Extractor vs Window

[RizzoTheRat]

We have an extractor fan in the bathroom.

After having a shower I leave the extractor on to pull damp air from the room, which is presumably replaced with drier air leaking in around the door.

The Mrs on the other hand always opens the window after a shower. To my mind that just dumps cold air in to the room and causes all the moister to condense out.

So which is better?

[RizzoTheRat]

marshalla said:

Opening the window allows the humid air from the room to vent out and mix with the drier air from the outside, so the overall humidity in the room is decreased.

Does it, or does it let some warm damp air out and cold air dry air in, which mixes, drops the temperature of the rest of the air in the room and condenses out the moisture? The temperature certainly drops very fast with the window open, yet farts take ages to clear, so I'm not convinced that much air changes places.