You are (probably) wrong about randomness. I’ll show it to you. Let’s do an experiment. Pick up a pen, paper, or your favorite text editor, and manually generate a random sequence of ten characters, composed of ones and zeros. My guess is, your answer will be:
Randomness is incompressible. Li and Vitanyii offer an interesting variant on the higher order version of this in their wonderful book on Kolmogorov complexity: random sequences must include a small number of nonrandom sequences, otherwise their predictable absence would be a compressible restriction.