The student picked <em><u>his or her</u></em> own backpack and ran to math class.
Explanation:
Pronouns are those words that we use to replace nouns. This is to avoid the repetition of the nouns and to make the sentence smoother and easier to understand.
In the given sentence, the main subject is "the student". Now, we cannot know what is the gender of the student but it is understood that it will be either he/ she, which makes the required pronoun include both genders. And on that note, the pronoun for the 'student' will be used in the possessive determiners (his/ her) instead of the personal pronoun (he/she) forms.
