What are probabilistic and stochastic approaches?

Probabilistic and stochastic approaches are ways to think about things that don’t always go exactly as planned, like when you’re trying to guess what flavor ice cream your friend will pick.

Probabilistic means thinking about chances, like rolling a dice or flipping a coin. Imagine there’s a bag with 3 red marbles and 2 blue marbles. If you close your eyes and pick one, there's more chance it’ll be red than blue, that’s probability at work.

Stochastic is similar, but instead of just one event, it’s like when things happen randomly over time. Think about a toy car that moves forward sometimes and backward other times, it doesn’t have a fixed path, so we call its movement stochastic.

If you roll a dice 10 times, each number has the same chance to come up. That’s a probabilistic approach, knowing what might happen, but not exactly when. If your toy car moves randomly, maybe it goes forward 6 out of 10 times, that's like using a stochastic model to predict its path.

Both help us understand things that aren’t completely predictable, just like ice cream flavors or toy cars!