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The three-box problem (Section )
seems to be intuitive for some, but not for everybody.
Let us label the three boxes: , Golden-Golden;
, Golden-Silver; , Silver-Silver.
The initial probability
(i.e. before having checked the first ring) of having
chosen the box , , or is, by symmetry,
.
This probability is updated after the event `the first ring extracted
is golden' by Bayes' theorem:

where
,
and
are, respectively, 1, 1/2 and 0.
Finally, calling `the next ring will be golden if I extract it
from the same box', we have, using the probability rules:

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Giulio D'Agostini
2003-05-15