Weird Maths

[Fist and Faith]

I saw this years ago in Marilyn vos Savant's column in Parade - www.parade.com/askmarilyn/ - so I knew the answer. I don't remember the reasoning.

[I'm Murrin]

You're twice as likely to have been wrong in the 1/3 guess as you are to have been right.

[Fist and Faith]

Yup. But once one door has been opened, there would seem to be a 50/50 chance of picking the right door from the remaining two. So why does switching from the one you originally picked increase your odds?

[I'm Murrin]

It doesn't change the fact that your first guess was more likely to have been wrong.

Rather than a 50/50 choice, your options are "door you picked" and "everything you didn't pick", with resulting odds of 1/3 and 2/3 respecitvely.



To make it more obvious, lets say you have 10 doors. You pick one door out of 10, and then 8 other doors are opened to show the dud prize. Your options are the first door you picked, and the last remaining door you didn't. The chances the prize is not in that other door are quite obviously low.

[drew]

Me? Heh, I wasn't trying to be mysterious: here's one of them:

gwydir.demon.co.uk/jo/numbers/finger/multiply.htm

They teach the nine one in school around here. The six one looks insane!!!