Okay, you're in a game show that is akin to Deal or No Deal. You are given 3 suitcases to choose from, 1 of which contains a million dollars, the other two are empty. Once you have chosen a suitcase, the host (who knows beforehand which of the 3 suitcases contain the million dollars), opens one of the (remianing unchosen) suitcases of which he is sure is empty. You are then given the choice of switching the suitcase you chose with the other suitcase that is unopened. Prove that it is beneficial to switch suitcases. I am quite confused by this...I'm thinking that switching cases would give you a 50% chance of getting the million dollars, while not switching will only give you a third of a chance. But this does not make sense intuitively. help please.