The correct option is C his or her
A Pronoun is a word or phrase used in place of a noun. The pronouns ending with '-body' or '-one' such as everybody, anyone, anybody, etc are singular. Thereby, the possessive pronouns referring to these pronouns should be singular as well. 'Their' is a plural possessive pronoun and needs to be replaced by a singular possessive pronoun while referring to 'everyone'. Option C is the correct answer for this sentence, as we are not familiar of the gender in question. 'His' or 'Her' are singular possessive pronouns. We need a replacement for 'their' so Option D is incorrect. Option A and B mention his and her separately, hence, they are incorrect. So, the sentence will read: Has everyone booked his or her tickets?