Hello. Nice work, but there is a false assumption that you make in your calculation. You say, that the probability to pick from X is **p(X)**=0.5. But this is not true. The experiment says:

Every time the dice shows the number 4 or less we will pick an item from bowl

, for the number 5 or higher we will pick an item from bowlX.Y

Meaning there is a higher chance to pick from **X**. Statistically speaking, in this case, we would expect to pick 4/6 of times from **X**. But this also is not very likely. Because we only have 300 samples, our value of P(X) would differ from 4/6. **P(X)** would only converge against 4/6 if we pick an infinite amount of samples. In this article, I use the value of **P(X)**=2/3 to highlight this case, which differs from your **P(X)**=0.5 case.

And because you assume that the probability is 50% for a random bowl, your **P(B)** also differs from what I calculated in the experiment.