I will post this all day if I have to:
The answers to all wait list questions are on the The Wait List thread pinned at the top of this forum, but are summarized best here:
http://talk.qa.collegeconfidential.com/discussion/comment/21211847/#Comment_21211847
And, no, applicants are not taken off randomly. They are chosen by best-match to fill the holes left by those who chose not to matriculate. Because you can never know what those holes are, you can never know your chances of coming off a waitlist.
Also, there is not a one-to-one correlation between one person who chooses not to attend a school and one person coming off the WL. A school will not go to its WL until if finds itself under-enrolled. For example, based on historic yield, a school may know that it needs to send out 250 admit letters in order to fill its 200 spots. So, only after the 51st applicant turns down admission will the school need to look at the WL.