Filtered probability space

Hey there, kid! So, you know how sometimes we toss a coin and we get either heads or tails? That's called a probability space because we know there are two possible outcomes.

Now, let's say we're playing a game where we can roll a dice and get a number from 1 to 6. But, we don't see the number right away. Instead, we have to go through a maze and every time we move, we get a clue about what the number might be.

That maze is like a filter. It helps us narrow down the possibilities. And, when we finally get to the end of the maze and see the number on the dice, that's like the outcome we're looking for.

So, a filtered probability space is when we have a bunch of different filters (like the maze) that help us figure out the outcome we're looking for. It's like we're taking a bunch of clues or information and using it to make a guess about what the final result will be.