Respuesta :
The only correct sentence is sentence A.
Aunt Betsy somehow made it to her thirtieth birthday without changing a lightbulb; in fact, she didn't even know what one looked like.
A semi-colon is used appropriately to separate two independent clauses. The other sentences are not correct. You need to have a complete sentece before a colon, which is why sentence B is incorrect. In sentence C, the semi-colon should be a comma. Similarily, in sentence D, the semicolon should be a colon.