✅ The correct answer is B) "their." The antecedent is "board of directors," which is a collective noun. While collective nouns can be treated as singular when acting as a single unit, they take a plural pronoun when referring to the individual members acting separately.

The phrase "individual opinions frequently diverge" explicitly indicates that the members of the board are acting as distinct individuals, not as a single, unified entity. Therefore, a plural possessive pronoun is required to agree with the implied plural number of the individual members. (Formula: If Collective Noun acts as individuals → use Plural Pronoun).

❌ Option A) "its" is a singular possessive pronoun. It would be correct if the board were acting as a cohesive, single entity (e.g., "the board submitted its report"). However, the context here emphasizes individual actions.

❌ Option C) "his or her" is a singular possessive pronoun referring to an individual person of unknown gender. It is not appropriate here because the context implies multiple individuals acting, not just one, and the antecedent, though a collective noun, is functioning as a plural in meaning.

❌ Option D) "one's" is the possessive form of the indefinite pronoun "one." It does not refer back to the specific antecedent "board of directors" or its members in this context.