I have a question about what types of situations we are able to assign a probability. Let me make up a hypothetical scenario here that roughly gets at what I'm trying to understand.
MY PREMISE: Suppose we know that there exists 1 billion red marbles in the world, and furthermore we know that every one of these marbles was invented and produced by Bob. These are the only red marbles that we are aware exist. Now suppose that we find a new red marble.
MY QUESTIONS: What is the probability that this new red marble that we have discovered, was made by Bob? And how do you come up with that calculation? Is it even possible to assign a probability to this situation?
Now, if we can't figure out a probability to this situation, I have a few follow up questions:
A) Why can't we assign a probability to this situation?
B) Can we even say that it's more likely that the red marble was made by Bob, than not made by Bob? My intuition about this question says yes, it does seem reasonable to say that it is more likely that the red marble was made by Bob, than unlikely. But I'm also aware that intuition is often wrong in cases like this, which is why I'm asking what the mathematics and logic says about this.
C) What if we knew that Bob had made 5 billion red marbles (as opposed to 1 billion)? Is it more likely now (compared to Bob only having made 1 billion) that the new red marble was made by Bob?
By the way, feel free to change my hypothetical scenario or use a different example if it helps to get at the heart of the question I'm trying to understand here. And thanks in advance for any insights you can provide.