Can we Conclusively Prove that a Theory is Mistaken?

Karl Popper stressed that, although a theory can never be proven to be true, it can be decisively disconfirmed if it makes a prediction that turns out to be false. Bayes' Theorem accommodates this insight. Consider again the marbles from Joe's. The generalization that all the marbles are black predicts that the next marble will be black (which implies that it will not be yellow, white, or any other color incompatible with being black). You draw a marble from the bag and find that it is yellow. What is P(E|T)? Assume that you were agnostic to begin with, and that 20\% of the marbles in the bags that are not all-black are yellow. What happens when you plug in the numbers?

Did you get 0? I did. Does this show that a theory can be decisively disproven by an experimental result? In a sense, perhaps. But notice that we are presupposing a good deal of background information that could turn out to be mistaken.