The decision in this 1945 federal case put an end to the discriminatory "white primaries" in Georgia

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Yes ... it totally did

Explanation:

Smith v. Allwright, 321 U. S. 649 (1944), was a landmark decision of the United States Supreme Court with regard to voting rights and, by extension, racial desegregation. It overturned the Texas state law that authorized parties to set their internal rules, including the use of white primaries.

White Primary. A state primary election that restricts voting to whites only; outlawed by the Supreme Court in 1944