Let's assume we're living in a mechanical deterministic world. Now do you agree that any uncertainty is a result of lack of knowledge? We flip a symmetric coin. The equations of movement are deterministic, but the outcome is uncertain, with probability 50% tail or head. Thus, it's the initial state that is unknown and makes the uncertainty. How is it that the initial state is in 50% of times in favor of tail and 50% of time in favor of head? Now, this initial state which comprises of the initial velocity vector, initial position, air turbulence, etc... is itself an outcome of the past deterministic processes that has happened through deterministic equations, but with uncertain 2nd level initial state that has been with probability 50% in favor of initial state that leads to head, and 50% in favor of initial state that leads to tail. We can continue this questions infinitely or go back to the beginning of the world. my question is, where does this 50-50 distribution (or any other PDF in general) comes from?