A uniform prior

We might enter the experiment with no expectations about how well or how poorly participants will perform.

Now, we observe one trial: a success!

This changes our belief about the probable probabilities of success: we know it can’t be zero, because we just saw a success.

In fact, here’s how our belief about every probability looks now, superimposed over our prior:

Let’s let a couple more trials trickle in:

And even more…

What is happening here?