How likely is it that I will be induced?

I am 39 weeks tomorrow. I was checked at 38 weeks and I was 1cm, 50% effaced and at a -2 station. Today at 39 weeks I was checked and haven't changed. My next appointment is monday and I am pretty sure they schedule me for induction about a week after that. I am so nervous. I just want to start labor on my own but really what are the chances I will go by my due date with this little of progress?

Slim. It's rare for a woman to give birth on her EDD

I had my 38 week appointment on friday, I was 38 weeks 5 days. I was only 1-2 centimeters dilated and 50% effaced. Pretty sure baby wasn't too far down as well. On sunday morning, 39 weeks exactly, my water broke. So anything is possible.