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# Marbles in a cup question

there are two blue marbles in one cup. two red marbles in second and one blue one red marble in a third cup.

the three cups are labeled blue-blue, red-red, and blue-red. none of these labels correctly describes the marbles in that cup. by reaching into cup of your chocie and pulling out one marble without looking at the other, how can you determine, without a dought, the color of the marbles in each cup?

Asked by CURIOUS 5 years ago

### 1 Answer by Expert Tutors

John R. | John R: Math, Science, and History TeacherJohn R: Math, Science, and History Teach...
4.6 4.6 (55 lesson ratings) (55)
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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