The universe is deterministic, thus no free will. The brain is merely an object which follows the laws of physics and chemistry.

TL;DR: We are moist robots. Our “choices” are made by the state of chemicals and neurons in our brain at a given moment, and those chemicals and neurons are affected by our genes, environment, past experiences, and external stimuli, none of which we have control over.

Back to your example of the green ball and red ball, when you present person X with that choice of selecting one or the other, you are basically subjecting his brain to an external stimulus over which he has no control. Lets call this external stimulus E.

Like a finite-state machine, this person’s entire life and experiences will have caused his brain to be in one of two sets of states, lets call these two sets of states A and B.

For any brain-state in group A, if the brain is presented with external stimulus E that will cause a chain reaction in the brain which will have repercussions that extend to the eye and the hand and cause them to take the red ball.

For any brain-state in group B, if the brain is presented with external stimulus E that will cause a chain reaction in the brain which will have repercussions that extend to the eye and the hand and cause them to take the green ball.

Crude as this example is, you can definitely extend it to any situation. Selecting an item from the menu at a restaurant, for example. The “choice” you make will be entirely dependent on the state of the chemicals and neurons in your brain at that very moment. And those chemicals are affected by many things, none of which you have control over such as:

1- The state of your stomach i.e. how hungry are you

2- What you had the last time you were there. The chemical effect from last week will still be there

3- Whatever the person your with is having will also affect your brain chemistry

If you wish to refute my theory please tie your examples in some way to Christian texts