spaf@gatech.UUCP (08/25/83)
All of the explanations I have seen for the coin selection problem
are of such complexity that the only ones who could understand
them were the people who solved the problem correctly in the first
place. Let me try an explanation which might be more accessible.
The reason the probability is not 1/2 is due to the fact that you
don't know if it was the top or bottom drawer you opened. If the problem
stated that you opened the bottom drawer and found a gold coin, then
the probability is indeed 1/2 that the other drawer contains a gold coin.
Let's remove the possibility of order coming into the question.
Consider 3 rooms with 2 people in each: Ann and Amanda in one room,
Bob and Betty in a second room, and Carl and Chet in the third room.
If you blindly open a door and take someone out, and you see that they
are male, what is the probability that the other person in that room
is male?
Obviously, you didn't open the door to the room with Ann and Amanda.
Therefore, you got either Bob, Carl, or Chet. That leaves the other two
men and Betty unselected. You could end up choosing any one of
those 3, two of whom are male. Thus, 2/3.
Is that clearer?
--
The soapbox of Gene Spafford
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