The calculation for a 50–50 probabilities would be too easy. I wanted to make it more interesting. That's why I chose to different probabilities.

In this case with the new value for **P(X)**, your final result will still differ from the calculated result in the experiment. Both ways are correct, however.

In your case, you are using true values of all required probabilities, by using the knowledge of how many blueberries and oranges there are in the bowls.

I wanted to present the other approach, by picking samples and calculating approximate values of these probabilities. The reason why I did this, is because in reality you almost never have the knowledge about the true probabilities and you are forced to do some kind of sampling.