Table schema:
CREATE TABLE table_name_15 (winner VARCHAR, year VARCHAR, country VARCHAR, score VARCHAR)

Question: What is the total number of 1st prize ($) that has a United States country with a score lower than 271 and in a year after 1964 with a winner of Bobby Mitchell?
SQL: SELECT COUNT(1 AS st_prize___) AS $__ FROM table_name_15 WHERE country = "united states" AND score < 271 AND year > 1964 AND winner = "bobby mitchell"