rush

how often does it happen that a girl who probably should've received a bid from a certain house and truly does belong there does not end up receiving a bid?

20% of the time? Sororities are huge- choosing 80 girls out of 2000 a year is massive. Having girls with bad judgement make decisions, a girl representing herself amazingly in recruitment and terribly in real life... at least 10-20% of sorority girls in most houses would fit better elsewhere. And then plenty of girls get cut from okay-bad houses presuming they'll end up somewhere top tier and end up cut from almost everywhere. It's not a very functional system. Sorry for the pessimism but.....

Uh.
Idk if you can really assign a percentage to that.
But, there isn't one specific house a girl belongs to from the beginning. You can't meet someone and go "Oh yeah she's a KKG" or "Oh she's so SK". When people say trust the system, and that you will end up where you belong, it's not because there is one specific house you belong too. I am sure most girls in a sorority could get along well in more than just one house. They say that you will end up where you belong because out of 200+ girls, you are more than likely going to make amazing friends, no matter where you end up. Obviously there are girls that don't stick around because of rep, or don't give the house a chance, but if all girls stuck it out for at least a year in their house, the majority of girls would end up belonging to that house, because it's very hard to not make friends with 200+ options. When girls "do not belong" it tends to be because they didn't give the house a chance. Disregard tier and reputation, and try your hardest to be involved with the sorority, and you will more than likely feel like you've found your home, no matter where you end up.
If that makes sense.