Three boxes each contain two coins: two gold (gg), two silver (ss), and one silver, one gold (sg).

probability/three.boxes New

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Problem

Three boxes each contain two coins: two gold (gg), two silver (ss), and
one silver, one gold (sg).  A coin is taken from one of the boxes at
random.  It is SILVER.  What is the probability that the other coin in
that box is SILVER also?

Show solution

In article <banghar4-1702951116550001@403cc-mac-16.cl.msu.edu>,
Rick Banghart <banghar4@studentb.msu.edu> wrote:
> 50/50

Here are two variations to think about (call the original version (1)):

        (2) Same as (1), except the first coin is GOLD.
            What is the probability that the other coin is GOLD?

If your answer differs from your answer to (1), explain why.

        (3) Same as (1) and (2), except that you don't get to
            see the first coin until after you answer the following
            question:

            What is the probability that the second coin is the same
            as the first?

Again, if your answer to (3) differs from your answers to (1) and (2),
explain why.

Now consider (3) as if you were seeing it for the first time, without
regard for variations (1) and (2).  Surely the answer to (3) must be
2/3, since two of the three boxes contain like coins.

Could there be something wrong with one of your answers?  Which one?

-- Dave Seaman <ags@seaman.cc.purdue.edu>

[ Editor: Seaman's argument implies that the answer to the original
question is 2/3, not 50/50. ]