Hard to say.
A few factors:
1. Your position on the alternate list. If your #1 on the alternate list then your chances are way better than being #5.
2. The closer it gets to the school year starting then your chances diminishes more. More people typically turn down an acceptance if they get accepted somewhere else earlier in the process. Once you start getting to July/August, the majority have already sorted out housing arrangements and solidifying plans.
Nonetheless, you never know what happens! We had one person drop after the first day of orientation, just felt like it wasn't for him. They called another guy as he was on an international trip and he rounded back to start on the 2nd day of orientation. Wild.