Below is the list of tables from the database along with their columns and datatype. Need to generate an accurate SQL query for the question.
Only use the columns present in the respective table. Only use the columns which are required to generate the SQL query. Only use table joins if required and not otherwise.

### Tables ###
TABLE: CREATE TABLE table_71110 ( "Year" real, "Winner" text, "Country" text, "Score" real, "To par" text, "1st prize ( $ )" real )

### 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?

### Accurate SQL ###

SELECT COUNT("1st prize ( $ )") FROM table_71110 WHERE "Country" = 'united states' AND "Score" < '271' AND "Year" > '1964' AND "Winner" = 'bobby mitchell'