Yes, white privilege does exist and it's horrible how black people are treated now a days especially in their everyday lives but no one wants to do anything because it isn't affecting them personally. Until people can realize that we're all the same loving race, we're never going to achieve equality, peace, and a likeable society.
Edit: I will say though, I never felt afraid of the police until the Mike Brown and Eric Garner incidents showed me how corrupt the police force can be. Now I'm not saying I'm paranoid about it in my day to day life, but the thought is in the back of my head.