Pick a colour...

Here's another of those counter-intuitive problems I like to tease you with.  I show you three cards - one is black on both sides, one is red on both sides and the third is black on one side and red on the other.  We place them on the table under a cloth, shuffle them about and then slide out one at random.  We observe that the side we can see is red.  I say to you "Well, obviously this is not the card that is black on both sides.  It is either the card that is red on both sides, in which case the other side of this card is red, or it's the red/black card in which case the other side is black.  It's just as likely to be one as the other so it's a 50-50 chance.  But I have a fancy that the other side is red, and indeed I'm willing to back my fancy by offering you odds of 6/4 against it being black - so to be clear, if you accept my bet and the other side is black you will win one and a half times your stake".  Should you accept my bet?  Watch this space.