Six checkers are placed in three boxes:

- Box "RR" contains two red checkers.
- Box "BB" contains two black checkers.
- Box "RB" contains one red and one black checker.

How can you determine the correct contents of all three boxes by taking only one checker out of one of the boxes (without looking at any of the other checkers)?

Question

20-07-2024
Mathematics

High School

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Six checkers are placed in three boxes:

- Box "RR" contains two red checkers.
- Box "BB" contains two black checkers.
- Box "RB" contains one red and one black checker.

How can you determine the correct contents of all three boxes by taking only one checker out of one of the boxes (without looking at any of the other checkers)?

Answer :

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aboouthaymeen5 aboouthaymeen5 · Answer 1 · 2023-09-08T10:38:25-04:00

Answe and Step-by-step explanation:

Looking at the question the way it was asked, it is easy because it said they have been labelled, so you don't have to stress yourself. Although, if what is intended is, the labelling got wrong along the way and how do you identify the correct one? Then this is what to do:

Go to the one labelled RB. Since I'm assuming that the labelling got wrong, if you pick a red, it means what we have should be a RR and if we picked a black, it means what we have is a BB and we can't have a RB because it was labelled wrongly.

Let's assume he saw a red,

We know that the BB box was labelled wrongly, and we already determined that the box with RB is a RR. Therefore, the box BB can never be RR(because we've seen it already) and it's certainly not BB (due to the fact that they were labelled wrongly). So we have only one option left which is it being RB and whatever we have left will be BB.

If we assume what was picked from the wrongly labelled RB is black.

We know that the RR box was labelled wrongly, and we already determined that the box with RB is a BB. Therefore, the box RR can never be BB and it's certainly not RR (due to the fact that they were labelled wrongly). So we have only one option left which is it being RB and whatever we have left will be RR.