A box contains 12 balls, some black and some white. If you take 2 balls at random without replacement, the probability of getting 2 black balls is 1/6. How many black balls are in the box?
There are 4 black balls in the box.

Here's the reasoning:

1. We know that the probability of picking 2 black balls is 1/6.
2. Let's denote the number of black balls as B and the number of white balls as W.
3. Since there are 12 balls in total, we have B + W = 12.
4. The probability of picking 2 black balls without replacement can be represented as: (B / 12) * ((B - 1) / 11)
5. We know this probability is equal to 1/6, so we can set up an equation: (B / 12) * ((B - 1) / 11) = 1/6
6. Solving for B, we get B = 4.
7. Therefore, there are 4 black balls in the box.