Of the 3.1 million youth age 16 to 24 who graduated from high school between January and October 2011, about 2.1 million (68.3 percent) were enrolled in college in October 2011. The college enrollment rate of recent high school graduates was slightly lower than the record high set in October 2009 (70.1 percent). For 2011 graduates, the college enrollment rate was 72.3 percent for young women and 64.6 percent for young men. The college enrollment rate of Asian graduates (86.7 percent) was higher than for recent white (67.7 percent), black (67.5 percent), and Hispanic (66.6 percent) graduates.
So more female than male high school graduates enrol at college (72.3% vs 64.6%) and more Asian high school graduates enrol at college than whites (86.7% vs 67.7%). A white high school graduate is no more likely to enrol at college than a black or hispanic graduate (all roughly around the 67% mark).
So if one measure of privilege is who gets to enrol at college having completed high school, then Asians and females are doing best.