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So I recently finished an examination (so this isn't cheating!) and this was one of the questions asked. This exam was autograded by a computer so I want to see if this is a mistake by me or the computer.

You have three cards. One is black on both sides. One is red on both sides. One is red on one side and black on the other.

You pick a card randomly. Given that you have a card whose upper side is red. What's the probability that the other side is black?

I said the answer is $1/2$ since there are only two cards that are red and since you know one side is Red already, then the probability that the other side is black is $1/2$ since there's only one card of the two reds that has black on the other side.

But the computer said that this is wrong. Who is right and why?

Thank You

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    $\begingroup$ the computer is right, although it should not have used the phrase "the upper side" -- can you verify that? it should have said something like "the side you see" to remove ambiguity. $\endgroup$
    – hunter
    Mar 4, 2021 at 3:35
  • $\begingroup$ It did say upperside, but now I see it's one third, I did not think about this. Thank You $\endgroup$
    – user890187
    Mar 4, 2021 at 3:38

1 Answer 1

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You are wrong. Rather than cards you should focus on sides.

Each side is equally likely to have been seen.

You have seen a red side. There are three of these but only one has black on the flipside.

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  • $\begingroup$ I see, so it's one third, dang. Thank you so much. I understand now. $\endgroup$
    – user890187
    Mar 4, 2021 at 3:38

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