Whatever your parents answer is, be sure that you respect the decision whether you like it or not. Even if they say no, eventually you will move out and be able to make your own decisions.
My mom HATES snakes but she has changed quite a bit after meeting my ball python. Last night she came over and watched my snake for a bit. The woman who used to be extremely afraid of snakes now calls my snake "cute". She was even excited for me when I told her that the BP ate for the first time!
That being said, don't just go out and buy a snake hoping that they will change their minds. I waited until I moved to an apartment to get a snake. Remain calm when presenting them with information. Show your parents that you are responsible and have done plenty of research!