How many seconds have you been in the room?

Let's say the time between t1 and t2 is 1 trillion seconds. Let us further assume that all people go through the rooms in the same amount of time (thus people spend 1 second each in room A, and 1 million seconds each in room B).

100 trillion of the 100.1 trillion observer moments between 0 and 1 seconds in a room occur in room A. All of the observer moments past 1 second occur in room B (this is somewhat flawed in that it is possible that the observers don't all spend the same amount of time in a given room, but even in the case where 100 million people stay in room A for 1 million seconds each, and the rest spend zero time, an observer who's been in a room for 1 million seconds is still overwhelmingly likely to be in room B. So basically the longer you've been in the room, the more probably you should consider it that you're in room B).

If an observer doesn't know how long they've been in a given room, I'm not sure how meaningful it is to call them "an" observer.