Since you know that each cup is marked incorrectly, you should reach into the cup labeled blue-red. There are two possible results from this:
1. The marble is red. This means the blue-red cup should have been labeled red-red. Since the cup that is labeled blue-blue cannot be blue-blue (since it is mislabeled) and cannot be labeled red-red (since that cup has already been located), it should
be labeled blue-red. The remaining cup (originally labeled red-red) should be labeled blue-blue.
If marble from blue-red is red:
blue-red --> red-red
blue-blue --> blue-red
red-red --> blue-blue
2. The marble is blue. This means the blue-red cup should have been labeled blue-blue. Since the cup originally labeled red-red cannot be red-red (since the label is wrong) and cannot be blue-blue (since that cup is already located) the cup should be labeled
blue-red. The remaining cup (originally labeled blue-blue) should be labeled red-red.
If marble from blue-red is blue:
blue-red --> blue-blu
red-red --> blue-red
blue-blue --> red-red