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Probability problem

I found the following problem in Rosen's Discrete Mathematics and Its Applications 6th ed.:

There are three cards in a box. Both sides of one card are black, both sides of one card are red, and the third card has one black side and one red side. We pick a card at random and observe only one side.

If the side is black, what is the probability that the other side is also black?

Shouldn't the answer to the question be $1/3$, as among $3$ cards only $1$ of them has both sides black. But the book says answer is $2/3$, do I miss anything?

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    @David [here it is again](http://math.stackexchange.com/questions/132722/probability-problem)2012-05-16

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An informal way of seeing it is that there are $6$ sides, and we are observing a randomly chosen side. Of the $3$ sides that are black, $2$ belong to the double-black card.

We can alternately do a formal conditional probability calculation. Let $DB$ be the event that the card picked is a double-black, and let $OB$ be the event that we observe a black. We want $P(DB|OB)$. By the usual formula, $P(DB|OB)P(OB)=P(DB\cap OB).$ We have $P(OB)=\frac{1}{2}$ and $P(DB\cap OB)=P(DB)=\frac{1}{3}$.

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    @sven.hedin: Yes, perfectly correct. By the way, intuition should show that the answer of $1/3$ could not be right, since observing a black side *increases* the chances that we are dealing with the double-black.2012-05-16