Look at the notes of the chord. In an open E chord you have, from fat e to thin e, E,B,E,G#,B,E. And in the E scale(major) ther notes are E,F#,G#,A,B,C#,D#,E. The basic formula for an arpeggio is -root, 3rd, 5th, 9th(or octave). To hear this formula and how it soungs just play an open E chord, then only play the bottom four strings. Up than back. lowest to highest, than back to lowest. That is a basic E major Arpeggio. If you know scales or can name the note of a chord, you can figure out this stuff. Remember to make a chord you play the odd numbers in a scale. 1,3rd,5th,7th,9th,11th, and so on.