What kind of experience do I need to study a Bachelor's degree in media and arts?

I would like to go study a Bachelor's degree in media and arts. My dream is to be an animator or a game designer but I'm not sure if I'll be good enough when I apply to study. I started practicing drawing just about 3 months ago. I know it sounds weird but I really want to do that for a living already. Of course my plans could change tho. I'm 16 and I started studying in high school a few months ago so there's still almost 3 years to go. If then I'm still interested in drawing I'd like to go study for bachelor's degree in media and arts. To apply I need to submit a "pre-task" which will be rated pass/fail. So my question is, do you think I'll have the skills needed to create a good enough artwork to be able to study for a Bachelor's degree in media and arts? I have 3 years to practice but is that enough? (My current drawing skills are pretty terrible and I don't usually learn new stuff quickly. I don't have natural talent in drawing but I enjoy it a lot.)