Why are you insisting on bringing up prediction?
Because it matters.
It doesn't matter that you don't actually have the information. It exists whether you have it or not.
Somehow you seem to be missing the point. Let me try to simplify.
You're familiar with the Schrodinger's cat thought experiment... right? Well in the Schrodinger's cat thought experiment we lack information about the state of the particle. It's not just that we don't know the state of the particle, it's that the particle has no fixed state, and it won't have one until after it's measured. Until then it only has a probability.
The odd thing is, that this isn't just true for fundamental particles, it's true for everything. Until something has actually happened, there's never enough information to determine with absolute certainty what's going to happen. Ever. The probability is never 100%. The entire universe can be described by a wave function with a certain probability, and that includes whether or not you're going to have coffee or tea.
Quantum mechanics would seem to tell us that reality isn't deterministic... it's probabilistic. It's just that from our vantage point it certainly looks deterministic.
I'm assuming I'm correct because of the laws of physics (at the level at which we are talking), my everyday experience (and everyone else's) for the whole of my life.
But that's the whole point. Your everyday experience is wrong.
Yes, you're always gonna be able to trace the chain of cause and effect back through the antecedent conditions. So from experience the macro world is always going to look deterministic. But while it's always deterministic looking backwards, it's never deterministic looking forwards, and it's not because you don't have enough information. It's because the information simply doesn't exist. All that exists is a probability. That probability may be extremely high, but it's never 100%.
It's the same way with whether you'll choose to have coffee or tea. Looking backwards the causal chain may seem obvious, and it may also seem obvious looking forward. But quantum mechanics says that the probability is never 100%. Hence whether you'll choose to have coffee or tea is never absolutely certain until you've actually chosen to have coffee or tea. It wasn't certain yesterday, or an hour ago, or five minutes ago.
The question is, when it comes to our choices, what determines the final transition from probability to actuality? Is it merely random chance as it appears to be with the particle in Schrodinger's cat, or could it be that the mind plays a role in the transition from what you might do, to what you actually do do?