An interactive task to explore how data helps us infer the state of the world.
Imagine a box containing 10 marbles: 2 are blue and 8 are red. We're going to draw 10 marbles from this box one by one, putting each one back after noting its color (this is called "drawing with replacement").
Our Box:
Your single observation:
Below is a histogram showing how many times we get 0, 1, 2... or 10 blue marbles if we repeat the 10-draw experiment thousands of times. This reveals the true probability of each outcome for *this specific box*.
Now, let's switch to a different box. This one has an equal number of marbles: 5 are blue and 5 are red. See how the likely outcomes change.
Our Box:
Your single observation:
As before, the histogram shows the probability of each outcome. For this 50/50 box, observing 5 blue marbles is the most probable outcome.
Here we pre-calculate the probabilities for 9 different possible boxes, from a box with 1 blue marble to one with 9. Each chart below shows the **distribution of outcomes** (0-10 blue balls observed) for a specific box configuration.
This is the key step! We flip our perspective. Instead of asking "For a given box, what outcomes are likely?", we ask: "Given the data I saw, which box is the most likely source?"
Each chart below is for a fixed observation (e.g., "I saw 3 blue balls"). The bars show how probable that *one specific outcome* is for each of the 9 different boxes. This is the likelihood function.