Identify the mistake in this statement: "Does everyone have their train tickets ready?"

The statement "Does everyone have their train tickets ready?" employs the word "their" in reference to "everyone." In standard English grammar, since "everyone" is a singular pronoun, it should be paired with singular pronouns for possession. Thus, "his or her" would be the grammatically correct term to match the singularity of "everyone."

Using "their" in this context has become common in modern usage to promote gender neutrality and can often be accepted in informal contexts, but traditionally, "his or her" would be the proper construction. This illustrates a shift in language norms while still highlighting a significant grammatical consideration.

In contrast, the other elements of the statement, such as "does," "everyone," and "ready," do not contain grammatical errors. "Does" is the correct auxiliary verb for a singular subject, "everyone." "Everyone" is appropriately used in a sentence as an indefinite pronoun, and "ready" functions correctly as an adjective describing the condition of the train tickets.