Infinite divisibility (probability)
Let's imagine you have a pizza. You can divide the pizza into pieces, right? Now imagine you take one of those pieces and divide it into even smaller pieces, and then take one of those small pieces and divide it even more. You can keep doing this, dividing each piece into tinier and tinier pieces, forever.
This idea of dividing something into infinitely many pieces is what we mean by "infinite divisibility." It's a little bit like a never-ending game of slicing a pizza.
Now, let's talk about probability. Probability is a way of measuring how likely something is to happen. For example, if you flip a coin, there are two possible outcomes: heads or tails. Each outcome has a probability of 0.5, or 50%, because there are only two choices and they are equally likely.
But what happens if you divide that 50% chance into smaller and smaller pieces? You might think that eventually, you'll get down to a probability of 0%, meaning that the event is impossible. But actually, with infinite divisibility, you can keep dividing that probability into smaller and smaller fractions that approach zero, but never quite get there.
So, even though it might seem impossible, with infinite divisibility, you can always keep dividing a probability into tinier and tinier fractions. It's like playing a game of slicing a pizza that never ends, but instead of slices, you're dividing probability into tinier and tinier pieces.
This idea of dividing something into infinitely many pieces is what we mean by "infinite divisibility." It's a little bit like a never-ending game of slicing a pizza.
Now, let's talk about probability. Probability is a way of measuring how likely something is to happen. For example, if you flip a coin, there are two possible outcomes: heads or tails. Each outcome has a probability of 0.5, or 50%, because there are only two choices and they are equally likely.
But what happens if you divide that 50% chance into smaller and smaller pieces? You might think that eventually, you'll get down to a probability of 0%, meaning that the event is impossible. But actually, with infinite divisibility, you can keep dividing that probability into smaller and smaller fractions that approach zero, but never quite get there.
So, even though it might seem impossible, with infinite divisibility, you can always keep dividing a probability into tinier and tinier fractions. It's like playing a game of slicing a pizza that never ends, but instead of slices, you're dividing probability into tinier and tinier pieces.
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