Which pronoun should be used in the sentence: "Neither of the players has lost (his or her, their) keys?"

The selected answer, "his or her," is correct because it maintains agreement with the singular antecedent "neither" in the sentence. When "neither" is used as a subject, it refers to either one of two players, which necessitates a singular pronoun. The phrase "his or her" is a compound pronoun that accommodates both genders, ensuring that the sentence remains inclusive while adhering to standard grammatical rules concerning number agreement.

Using "his" or "theirs" would not be appropriate here because "his" works similarly but lacks the gender neutrality of "his or her." The option "their," while increasingly accepted in informal contexts to refer back to a singular noun, can create ambiguity in more formal writing. Therefore, "his or her" is the best choice to maintain clarity and proper grammatical structure in the sentence.