What are the chances ?

[ladyalex]

My family have been arguing about this all day so i have decided to ask it on here and see what AB makes of it.

You have 3 cards in a box. One is red on both sides, one is white on both sides and the third one is white on one side and red on the other side.
You draw one card out of the box showing only one side. The side showing is red.
What is the probability of the other side of that card also being red ?

[Marijn]

Here you go.....
http://en.wikipedia.org/wiki/Bertrand's_box_pa radox#Card_version

[Gizmonster]

Joe-king: I suggest you read that link by notafish ....

.... I don't wanna sound patronising but you are wrong - that link explains it all nicely.

If you've heard of the Monty Hall problem, than you shouldn't have much of a problem getting to grips with this one .....

[factor-fiction]

Great link Notafish. Sorry if I made you a little cross by challenging you to challenge my answer- I was just keen for someone to find the flaw in my logic as although I felt pretty sure I was right I am always prepared to accept a better/alternative solution. (Which is why i moved from saying 50-50 to 2/3 when I read the early arguments.) If you are now convinced the answer is 2/3, all I need is Joe-king to agree too and I'll then be 100% certain the answer is correct!

[factor-fiction]

I initially came up with the same answer as Joe-king as it's an attractive intuitive approach.

But you have picked a face (you know exactly what that is- it's black)- you haven't picked a card (as you don't know what the card is- it could be BW or BB).

On the two available cards there are 3 black faces and one white face . You have picked a black face. That leaves two black faces and one white face. So the chances of the other face being black is 2/3.

Great question ladyalex.

[Marijn]

You didn't make me a little cross factor30.
I thought maybe you were being a little rude to me because you thought I was a man. You don't need to convince other people. :-)

[ladyalex]

Thanks again for all your responses.
Glad you liked my question, factor 30.
Hope I haven't caused too many arguments.
Thanks for the wikipedia link too.
ladyalex