Final answer:
The listing contract for the sale of Mr. Baker's home that Betty enters into would likely be invalid because she has not been legally appointed to act on her father's behalf. Only Mary, who was appointed by the court, has the authority unless she has formally delegated this power to Betty.
Step-by-step explanation:
When Mr. Baker was declared mentally incompetent and his daughter Mary was appointed by the court to act on his behalf, it created a legal guardianship or power of attorney that allows Mary to perform legal acts for her father. Later, Mary asked her sister, Betty, to manage their father's affairs. The validity of a listing contract for the sale of their father's home entered by Betty depends on her legal authority to act on behalf of Mr. Baker.
Assuming Mary's role allows for delegation, typically, she would need to formally delegate authority to Betty, often through a document that grants Betty the power to act in this capacity. Without such formal delegation, any contract Betty enters would likely be invalid. Therefore, the correct answer is C: No, because Betty has not been legally appointed to act on her father's behalf.