glg wrote:There is no benefit of switching in this one. It's similar to Monty Hall, but not the same. The teacher has announced an incorrect answer without knowing what your answer is, where in Monty Hall, Monty knows your answer and has to act accordingly.
Sorry, I said earlier, I like "gotcha!" riddles, which this one is because it's deliberately setup to remind you of Monty Hall
I'd have gotten this one wrong had I logged in over the weekend. With the original MH problem, I always think of it that there is a 66% chance the car is behind one of the two doors you don't choose, so when Monty reveals one of those two doors to you, there is still a 66% chance you were wrong with your first guess so you should switch.
This logic didn't help me much with this problem-- here I thought, there is a 66% chance the answer is b or c and teacher just told me it is not C so I should switch, right? Had to puzzle over this a bit myself-- the website posted was similar in that you can see how if Monty doesn't know what he's revelaling but randomly reveals one of the other two doors you end up in the same situation here where monty doesn't know what you chose.
As you say, the odds of the answer being b or c remains at 66% only if the teacher knew what you had chosen a purposely revealed either b or c. In the MH problem *every* random guesser gets the advantage from the revelation, it matters not what their first guess is because monty adapts to that first bit of info. In this case 33% of the random guessers in the class (those who had chosen c) ought to switch their answers to either A or B going from their initial odds of 33% to the revealed odds 0% to the final odds 50% chance of getting it right. Those that randomly guessed A or B go from initial odds of 33% to revealed odds of 50% with no motivation to switch (well, they're now 100% certain they should not switch to c which they wouldn't have been without the revelation).
It took me forever to wrap my head around the original MH problem-- finally when I tried to write some code to simulate it, I hit an if/else branch were it was obvious that one would be taken 2/3 of the time and the other only 1/3 of the time and it became clear to me. But even then I hadn't realized how important the conditions of the problem were.
Fun puzzle!
(dead_poet-- we're waiting for your puzzle-- well, *I* think you got the right answer anyway-- I suppose you're waiting for confirmation, but sounds right to me
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