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 X, for the number 5 or higher we will pick an item from bowl 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.

Deep Learning & AI Software Developer | MSc. Physics | Educator|

Deep Learning & AI Software Developer | MSc. Physics | Educator|