Mary has 3 boxes with Marbles. Eavh box is labeled so that she knows what is in each box. She has 1 box with 2 blue marbles, another box with 2 red marbles and a 3rd box with 1 red and 1 blue marble. Mary's little sister removed all the labels and she placed them back incorrectly.
IS it possible for Mary to reach for only 1 marble, look at it and determine which box is which?
Thank you for the help!
To answer this question, we need to analyze the possible scenarios and consider whether there is enough information for Mary to determine the correct labeling.
Let's consider the possibilities:
1. Mary chooses a blue marble:
- If the box is labeled "2 blue marbles," then the labeling is correct.
- If the box is labeled "1 red and 1 blue marble," then Mary knows this label is incorrect because she has not chosen a red marble.
2. Mary chooses a red marble:
- If the box is labeled "2 red marbles," then the labeling is correct.
- If the box is labeled "1 red and 1 blue marble," then Mary knows this label is incorrect because she has not chosen a blue marble.
Now, let's evaluate the possible outcomes. If Mary chooses a blue marble, she can correctly identify the box labeled "2 blue marbles," but she cannot determine which of the other two labels belongs to the remaining boxes.
On the other hand, if Mary chooses a red marble, she can correctly identify the box labeled "2 red marbles," but she cannot determine which of the other two labels belongs to the remaining boxes.
Therefore, Mary cannot determine which box is which by picking only one marble and looking at it. She needs to pick multiple marbles or find other ways to gather additional information.