I know that Sarada possesses Sharingan, but since her mother isn't an Uchiha, was there any chance that she may not have inherited Sharingan?
I believe it is presumed that the Uchiha clan before their destruction bred from within, considering their seclusion and secrecy of affairs, in order to diminish the muddling of bloodlines and ensure generations that are able to possess the power. If you recall the early episodes of Boruto, there was a slight hint to the idea thay Sarada may not be able to unlock Sharingan, since she was so far ahead of her classmates and caught on to everything else at an early age. Two factors added to this fear: the first obvious, and the second relates to a village in peace does not create enough pain or passion to unlock the Sharingan (a harsh stipulation for such a strong power). Sarada felt outcast to her father for not gaining his abilities only to learn it was a lack of hardship that hindered her. I believe the relationship between Sakura and Saske represents overcoming the fear of losing powers due to diluting them with other bloodlines, and proves that mixing blood(and thus abilities) allows for a stronger offspring, possesing abilities from both families. So yes, there was an ancient fear she would not posses the Uchiha power stemming from a recluse family heritage but it was disproven.
There is a problem though regarding the way Kishimoto-san has built the world of Naruto, the said problem being the fact that the Kekkei Genkai don't seem to have any regard for Mendelian rules of genetics. As far as I know there are no known members of the Uchiha clan that don't possess the Sharingan(and by that I mean shinobi belonging to the Uchiha clan that have been explicitly stated that they don't possess the ability), so I suppose we can assume that every Shinobi with a parent belonging to the Uchiha clan possess the ability to awaken the Sharingan.
TL;DR: As far as we know so far there hasn't been any member of the Uchiha clan without a Sharingan, so I think it is safe to assume that Sarada having the Sharingan is pretty much guaranteed as long as one of the parents is an Uchiha.
I think the question you ask is kind of misleading. You want to know what the chances are that a kid born to non-Uchiha parents (both) can awaken the Sharingan. The answer to that is NO. Sharingan is a blood-line limit found in the Uchiha clan. If two non-Uchiha individuals married and had children, then the children won't be able to awaken the Sharingan.
In the case of Sasuke-Sakura, Sasuke is an Uchiha and Sakura is not. However, Sarada has the Uchiha gene in her DNA. Therefore Sarada is able to awaken her Sharingan
Now to answer your EXACT question about a child inheriting the Sharingan from two non-Uchiha parents is damn near impossible. But if the child were to get an eye from an Uchiha member by transplant, it would then be possible if the child were able to control chakra perfectly and redirect maximum chakra to the eye. Having said that, it is a known fact that the Sharingan drains the chakra reserves considerably. So even if the child inherited the Sharingan he wouldn't be able to use it like an Uchiha.