Beads puzzle (1 Viewer)

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In one container there are two black beads, in another two white beads, and in a third there are one black and one white bead. They are labelled appropriately BB, WW, and BW. Someone moved the labels in such a way that for each container the label doesn't show its contents. Can you determine the contents of all three containers by withdrawing one bead from one container only?


Science Advisor
Homework Helper
Of course.
so the BB is either on WW or wb. THIS MEANS THAT IF YOU STICK YOUR HAND IN bb AND DRAW a Black one you have found the WB. that has a probability of 1/2 for jar and 1/2 for bead and they occur at once so 1/4. If you stick your hands in WW and you draw a White bead same scenarion...1/4 chance but you found the WB.

hold on, i think i see sometihng. im making it too hard.

only one draw. let's assume you stick your hand in BB and you draw a White. you could be either in the correct WW or correct WB. this means...that NO, you can not predict it exactly. at least i don't think so.

if you stick your hand in what can't be BB becasue of label and you pull out something different than a BB you can't choose between the two remaining...
Yes, you can...
(In white)
Pull a bead out from the container labeled BW.

If you pull out a white bead, it is the container with two white beads, the BB must be the black and white container, and WW contains two black. If WW contained the black and white beads, then BB wouldn't be mislabeled.

If you pull out a black bead, BW is the container with two black beads, the BB must contain just white beads, and WW contains both white and black beads.

Thus, pulling a bead out of BW gives you enough information to know the contents of all the containers.
Yes you can...

You take a bead out of the container now labeled as BW (infact it is either the BB or WW can). If you find a black bead then it must be the BB can and if you find a white bead then it is the WW can.
Kaer Fyzarc said:
You take a bead out of the container now labeled as BW (infact it is either the BB or WW can). If you find a black bead then it must be the BB can and if you find a white bead then it is the WW can.
Good. What about the other two?
wel say u found a white bead in the BW labeled container then u have 2 jars left with BB and BW since u found a WW then the container labelled WW must have 2 black beads in and the container labelled BB the black and white bead, (because u cant have BB containing 2black beads)
however if u found a black bead, ud kno the jar labelled BB must contain 2 white beads. i think.
if you take one out from fake BW you identified the WW or the BB.

let's say you picked a White you found the WW as being falsely labeled WB. in front of you are two left. one is labeled WW and the other is labeled BB. Both the WW and WB are lalse labels. what you are correctly left with are BB and WB.

BB is both in sample space and in fake smaple space, and since BB can't be labeled BB, BB must be labeled WW because you already eliminated WB.

with two identified it's common sense what third is.

That's smart. i feel dumb now.


Science Advisor
Gold Member
It is assumed that all 3 labels are wrong. Soooo, take the container labled WB and pull out one bead. Suppose it is black. Now we know that we have the container that has 2 black beads. Switch labels with the container that has the BB label. Now we have one container guaranteed to be correct. We also have one guaranteed to be incorrect since its label is still wrong. Set the correct one aside and switch the other two labels around and it will all be good. :smile:

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