Students in Florida may be permitted to take Advanced Placement Psychology in the coming school year, officials said Friday, a day after the College Board had revoked its support for the course in Florida, asserting that it had been “effectively banned” by the state’s Department of Education. AP Psychology, one of the most popular Advanced Placement courses across the country, has been the subject of the latest tug of war between the College Board, an influential nonprofit organization that oversees Advanced Placement courses and the SAT, and the state of Florida.