Final answer:
Danforth did not believe Mary Warren's testimony because it contradicted his belief in the guilt of the accused. He gave Francis and Giles the chance to provide an affidavit because their information aligned with his goal of proving a wider witchcraft conspiracy.
Step-by-step explanation:
Danforth might not believe Mary Warren's testimony because as the Deputy Governor, he was heavily invested in the idea that the accused were guilty of witchcraft. Mary's testimony, which accused the girls of pretending to be afflicted by witchcraft, contradicted this belief. Additionally, Mary's testimony would have undermined the credibility of the court and called into question the innocence of the accused, which Danforth was not willing to do.
On the other hand, Danforth gave Francis and Giles the chance to provide an affidavit because he perceived their information as beneficial to the court's cause. Francis and Giles had information that could potentially implicate others in the community, which aligned with Danforth's goal of proving that the witchcraft conspiracy went beyond just the accused girls. Therefore, Danforth saw value in giving them the opportunity to share their evidence through written statements.