Are the chances of a child inheriting Sharingan smaller if one of the parents isn't an Uchiha? 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.