You have an urn with a blue ball and a red ball. At each step, if you pick a blue ball, you add another blue ball to the urn, and if you pick a red ball, you add another red ball.
Use the slider to see what the proportion of the balls will be on average after 50 steps. You can see up to 100 distributions. You should find out that any proportion is equally likely on average, even though when you start to draw many balls of one color you are likely to draw even more balls of that color. This process is called past-dependant and can be used to model many phenomena in real life.