Odds of Getting In
If you're the wrong fit, they'll know immediately (source).
There aren't any statistics out there on the number of applicants "accepted" to the monastery. This isn't like a college admissions process where you write a five-paragraph essay about your cat. Monasteries don't send pamphlets to your front door, trying to recruit the best, most promising future nuns and monks.
The process that most monasteries and convents use is a more free-flowing, individual, and discerning process. If you're a right fit for that particular establishment's mission and lifestyle, you won't be turned away.