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Card probability problem

The following question was asked on a closed online forum. I think the correct answer is 1/2, however the original poster insists that it's 1/3. What is the correct answer?

I have 3 cards, one black on both sides, one red on both sides, and one that is red on one side and black on the other. I shuffle the cards, select one completely at random and hold it up to you. The side of the card you see is red. What is the probability that the other side of the card is black?

  • 1/3
  • 1/2
  • 2/3
  • 1
    $\begingroup$ Does shuffling also include changing which side is up? $\endgroup$
    – Egbert
    Jun 2, 2012 at 11:46
  • $\begingroup$ @Egbert, no. (filler) $\endgroup$ Jun 2, 2012 at 11:48

1 Answer 1


The correct answer is 1/2. There are 3 card but 1 has both sides black. So given the face you see is red only 2 cards are possible. They are equally likely. So the chance it is black is 1/2.


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