Here's why:
* Antecedent: The antecedent is the word that the pronoun refers to. In this case, the antecedents are "musicians" and "conductor."
* Pronoun Agreement: The pronoun "their" needs to agree with the antecedent in number. Since "either...or" suggests a singular subject, we use the singular verb "knows."
Let me know if you have other sentences you'd like help with!