Answer:
Among the options given on the question the correct answer is option A.
She thought she wasn't smart enough to go to college, so there was no point in studying.
Explanation: The text describe in the question is a letter from Du Bois who was known an African American activist and was also a teacher. He wrote to a girl who was a student but she was hopeless about her study and did not attend the school.
In the text there is a indication that why she was hopeless . The possible reason is that she thought that she wasn't smart enough for going college. Because in the text it is said she thought she could not do anything in the world. This means that she thought herself she was unqualified.
However there is not indication of racial discrimination in the text as a reason of her hopelessness. Because the writer inspired her to join the work force and take the chance which is considered for African Americans by educating herself.
So, the possible reason for her hopelessness is that she thought she wasn't smart enough.