Recently I've been talking to a professor I highly admire and after a couple rounds of informal interviews, they've agreed to take me on as their PhD student and that I should apply formally to the university. They've told me to tell them once I've done so, so they can forward their recommendation to the folks at admissions that they'd like to take me on as their student. Talking to my peers and professors and given that I meet the minimum admissions requirement, I've been told that the chances of me being formally accepted is reasonably high.
However, I suppose I'm a bit nervous. Due to personal life circumstances, being accepted into a PhD program is quite important to me (albeit, this current program in question is my first choice by far given the nature of their research) but being from a third world country applications fees are very steep for me and I cannot afford to apply to more than a couple programs. In fact, applying to a second program will also be extremely difficult for me and I've left it as a "last case scenario".
I'd rather not air my personal worries (at least to this degree) to this professor lest I inadvertently give them the impression that I'm interested in their program for any other reason than being deeply passionate about their research (which is false - I'm beyond passionate about the work they do), but I would like to know if I have a decent chance of getting in or not so I can pull together the money and apply to another university as well.
TL;DR: Would it be appropriate to ask this professor how high of a chance I have as to being formally accepted by their university?
Thanks!