the corner office

a blog, by Colin Pretorius

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A card puzzle

Studying for an exam next week, I came across this courtesy of a kind professor in Hong Kong. I think it classifies as a bit of brain teaser, so thought I'd post it here:

Suppose we have 3 cards whose sides are coloured as follows:

  • red/red
  • black/black
  • red/black

A card is chosen at random and placed on the ground. If the upper side of the card is red, what is the probability that the other side is black?

The answer's in the comments...

{2010.01.26 - 16:40}


1 Colin (2010.01.26 - 16:51) #

The answer is 1/3.

If you thought the answer is 1/2 (as I initially did), you're missing the fact that each side of the red/red card contributes a 'chance', along with 1 from the black/red card.

(and the moral of the story is that probability and intuition don't always mix; if you calculated it the 'proper' way using a formula called Bayes' Theorem then you wouldn't have gotten the wrong answer, but you probably care less about that...)

2 Ronwen (2010.01.27 - 11:18) #

Yes, folks. It's non-stop fun at the Miller-Pretorius residence. :)


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