Indefinite pronouns (40e) often refer to antecedents that may be either male or female. Writers used to use a masculine pronoun, known as the generic he, in such cases. However, many people have pointed out that wording that ignores or excludes females should be avoided.

When an antecedent is a singular indefinite pronoun, some people avoid the generic he by using a plural pronoun.

Everybody had their own theories about Jennifer’s sudden resignation. [informal]

Although this usage is gaining acceptance, many readers still consider it incorrect. In formal writing, do not use a plural pronoun to refer to a grammatically singular indefinite pronoun.

Everybody had a theory about Jennifer’s sudden resignation.