One of the female players left __ hat in the locker room.
a. her
b. hers
c. its
d. their

The proper way of talking, is the way you can determine, what word fits into here.
let me see, 
one of the female players left her hat in the locker room.
why her?
well, because look, you are talking first of all of one person, so that makes it to be single. why not its, because that better refers to animals. 
why not their, because it is not plural, you are talking about one person not about a whole entire crowd.
So, I hope that this would help you better understand, this question.
The answer is A. Her
Hope you have a wonderful day!! =)