Richard Feynman wrote in "QED" on page 19 the following which is similar to what you are describing but about photons reflecting or not off of a pane of glass:
Philosophers have said that if the same circumstances don't always produce the same results, predictions are impossible and science will collapse. Here is a circumstance--identical photons are always coming down in the same direction to the same piece of glass--that produces different results. We cannot predict whether a given photon will arrive at A or B. All we can predict is that out of 100 photons that come down, an average of 4 will be reflected by the front surface. Does that mean that physics, a science of great exactitude, has been reduced to calculating only the probability of an event, and not predicting exactly what will happen? Yes. That's a retreat, but that's the way it is: Nature permits us to calculate only probabilities. Yet science has not collapsed.
Note that this behavior is not deterministic for a single photon. Nor is the probability of reflecting off a pane of glass like a random toss of a coin (which would mean 50 out of 100 photons should reflect, not 4). If one defined the ability to make a choice as behavior that cannot be determined nor is uniformly random, then each photon could be described as making a choice. Whether the photon actually makes a choice or not is left to philosophers to argue.
If a photon could be interpreted as making a choice, we should be careful before assuming that we cannot make a choice.
We fool ourselves because our models are simplifications of reality and they use mathematics which is deterministic. Those mathematical models we know must be incorrect because in those models we could go backward in time, but reality generally speaking does not go backward. The models give accurate predictions, but that does not mean that reality is the same as those models.
Here you are viewing yourself as an individual. It does matter what you think about reality because you influence the people around you. We are all members of various groups. We cannot isolate ourselves from all of these groups.