You are taking a multiple choice exam, where three answers are offered to each question. You have reached the final question. It is a real brain teaser and having no idea of the correct answer you randomly guess "B". Agreeing that the final question is inordinately difficult, the examiner announces that "C" is an incorrect answer. Do you switch your answer?

Absolutely, every time. What was that game show where there were three doors? This question is usually posed as a choice of doors in that game show. Had a friend once who insisted the choise was 50/50. Tried to get some money on the table but it never quite came togethor.

Depending on the assumptions made when the question is posed, the choice may be 50-50. You tell me whether Monty must offer the choice to switch every time, and whether he knows which door is wrong before he opens it and I will tell you the odds.

The question as posted here is not the same as the Monty Hall Dillema. In that problem it made sense to switch because that way you had a probability of 2/3 to win. In this case you must clarify if the examiner knows your guess and then reveals an alternative wrong solution. If not then the problem is different.

It depends whether you have already made a choice between A,B, or C. IF not, you now have two choices. The odds are 50/50. Changing your choice is nugatory. You simply have two choices with the elimination of the third choice. The game show was different: There are 3 doors, behind which are a car, and 2 goats. Your odds at the outset of selecting the door with the car are 1/3. You make your selection. Monty Hall, with knowledge of what is behind each door selects a door with a goat behind it and offers you the option of changing your selection. The question is whether changing your choice increases your odds, The answer is it does. Here is why: If you select the car at the beginning and change your choice, you lose. But your chance of having selected the car is 1/3 at the beginning. If you did not select the car, but a goat, which is a 2/3 probability and you change your choice, you must win the car, because Monty revealed the other goat Therefore if you change your selection, 2 out of 3 times you will win the car.

so how does this probability theory apply to the new game show "Deal or No Deal" when at the end you are offered the option of switching cases?

Search "Restricted Choice" on Google. This question comes up about three times a year. The solution is a simple application of Bayes Theorem. nitro