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One of my favorite logic puzzles, and one people get wrong all the time.
You're given three doors, A, B, and C. There is a prize behind one. If you choose the right door, you win the prize.
You choose a door and the host opens a door you didn't choose and shows there's no prize. You're given a chance to change your mind and switch your choice to the remaining unopened door.
Do you change your mind or not? Why or why not?
@ovid Change because if I’m damn well on national television dressed as a Baker with a sign that says “Monty I really need the Dough” … I’m gonna play it for all I got.
@ovid yes, because I've read the story before and past me understood her logic even if present me doesn't:)
@ovid The classic answer is that you should change your mind because the chance you picked the right door on the first try is one in three, meaning that the remaining door has a two in three chance of holding the prize.
However, this assumes that the game show host knows where the prize is. Monty Hall himself claims he didn't, and would just as often reveal the prize when the first door was open. In this case there is no advantage nor disadvantage to switching doors.
@tobyink @ovid Just because Monty (or now Wayne Brady) don’t know where the prize is doesn’t mean that a) Carol Merill didn’t get told which door by the producers who do know … and b) that winning the top prize is the only goal, if I recall it was a three levels of prizes … so avoiding the worst prize is still a better outcome.
@perigrin @ovid @tobyink It doesn't matter if they knew.
If they open the door and reveal the top prize then you have 0 chance of getting the top prize and your choice doesn't matter.
If they open the door and it isn't the top prize then that doesn't affect the outcome of the door you did pick, but it does give you info about the door you didn't.
Their knowledge isn't relevant.
@tobyink whether the host knows or not doesn’t change the logic.
@ovid You change your mind because new information has come to light. You originally had a 1:3 chance but now you have a 1:2 chance.
@saudonym not quite right.
@ovid yes, to change my chances from ⅓ to ½.
@smokemachine Your chances change from 1/3 to 2/3rds.
@ovid yes, sure! Sorry!
