Which of the following is a popular music genre associated with Kentucky?

Bluegrass is a popular music genre that has deep roots in Kentucky, making it the correct answer. Originating in the 1940s, bluegrass music is characterized by its use of acoustic instruments such as the banjo, mandolin, and fiddle. The genre reflects the cultural influences of Kentucky, drawing on traditional folk music, the Appalachian sound, and elements from jazz and blues.

Kentucky is often referred to as the birthplace of bluegrass, with legendary musicians like Bill Monroe, who is considered the "Father of Bluegrass," hailing from the state. Additionally, the annual International Bluegrass Music Association's awards and festivals held in Kentucky highlight the state's significant contribution to this genre, further solidifying its association with bluegrass music.

The other genres listed, such as jazz, rock, and hip-hop, while influential and popular across the United States, do not have the same historical and cultural tie to Kentucky as bluegrass does.