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. 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 'somebody' because somebody is a singular pronoun. Hence, this statement is not correct. As we are not familiar with the gender in question for the noun, here, 'the passengers'. we need to use 'his or her'. These are singular possessive pronouns and need to be used in place of 'their'. So, the sentence will read, Did somebody lose his or her belongings in the train?