(There is already a similar question to this question, but it has no accepted answer …, so ๐

There are two boxes indicated. There are 15 white and 12 black balls in the first box and 14 white and 18 black balls in the second box. Anna delivers the following experiment. Anna places her hand in the first box, immediately takes two balls and places them in the second box. Then she takes a ball without looking out of the second box.

**What is the probability that she took a white ball from the second box?**

My approach is to first calculate the probabilities of the 4 possible cases to move two balls: {(WW), (WB), (BW), (BB)}.

And then multiply the resulting probabilities by the new second box amounts. Finally, I would add the four resulting values.

For example. For (WW) I would do:

- Draw WW: $ frac {15} {27} * frac {14} {26} about $ 0.3
- Calculate the probability of drawing white from the second field: $ 0.3 * {frac {16} {34} about $ 0.14

But I'm not even sure if I have to differentiate between (B, W) and (W, B)