Your best bet for a statistic is to call your OB/GYN - I couldn't find anything on Google other than similar questions on similar parenting sites. I couldn't find anything on any credible medical websites.
But, my uneducated guess is that it's completely dependent on the pregnancy.
My first, I went into labor on my own just past 40 weeks.
My water broke with my second child. My OB's office put me off all day saying it was stress incontinence because I wasn't saturating a pad. Finally, after the 4th call, they sent me to the hospital who admitted me after confirming the water had broken, and had to induce me to prevent infection.
However, even the manual exams they give you later in pregnancy can accidentally knick the membranes and cause the water to break - happened to a former colleague where a routine visit at 38 weeks became an induction because the OB accidentally broke her water on an internal exam.
Good luck.