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You have 3 jars. Each jar has a label on it: white, black,
or white&black. You have 3 sets of marbles: white, black,
and white&black. One set is stored in one jar. The labels
on the jars are guaranteed to be incorrect (i.e. white will
not contain white). Which jar would you choose from to give
you the best chances of identifying the which set of
marbles in is in which jar?
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Answer Posted / aj
It doesn't matter... choosing any jar will give you a
complete solution, so they've all got the same odds (100%)
of identifying which set of marble is in which jar.
eg:
Three jars labelled white (W), black (B) and white&black
(WB)
Now pick any jar at random... eg: the one labelled W. From
the problem domain, this jar cannot have W marbles in it,
so it must have either B or WB marbles in it.
Working through the first possibility (that the jar
contains B marbles) means that there are jars with W and WB
marbles in them and the jars these jars are labelled B and
WB or WB and B respectively.
Again, as the jars are guaranteed to be labelled
incorrectly, this means that the WB marbles cannot be in
the jar labelled WB, so they can only be in the jar
labelled B. This leaves the W marbles to be in the jar
labelled WB.
You can follow this thought process through with any jar
and will find that you can always solve the problem by
looking in one jar.
The question is cleverly written to cause confusion by
having marble colours W & B and then a third colour which
seems to be a mix of the two, when in reality it is simply
a third colour.
| Is This Answer Correct ? | 4 Yes | 8 No |
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