This is a variation of a probability question (Bertrand's box, or the three card / two color question) that's been asked many times before. However, this question relates specifically as to whether or not a guarantee can change the outcome. Here is the exact wording of the question:
I have two cards, one with two blue faces (BB) and the other with one blue face, one red face (BR). I draw one of these cards at random, and I show you only one face of the drawn card. You observe that the face I've shown you is blue. What is the probability that the other side of the drawn card is also blue?
As you know, the answer is 2/3. However, I've recently had many colleagues argue that the wording of the question is ambiguous such that the answer would be 1/2 if I guaranteed you that the side I show you will be blue.
In other words, the claim is that changing the phrase "you observe that the face I've shown you is blue" to "I guarantee that I will show you a blue face" will change the probability from 2/3 to 1/2. In both situations, the card is still drawn randomly.
I can't wrap my head around this, and my colleagues cannot explain it to me in a way that is mathematically sound.
I think, perhaps, that this question is being confused with the Monty Hall vs. Monty Fall question. In the latter, the host slips on a banana peel and accidentally opens one of the non-chosen doors, which just so happens to reveal a goat. In this scenario, there is no advantage to changing doors -- even though the same information is seemingly revealed, the host is constrained differently in Monty Hall than he is in Monty Fall.
In contrast, the card situation seems to me like a straightforward Bayes solution. The information (blue face) is a given, and I do not see any reason why the ignorance of the question-asker would change the nature of the information. Can anyone offer insight as to how the guarantee does or does not change the question?