> There are three boxes:
> – a box containing two gold coins,
> – a box containing two silver coins,
> – a box containing one gold coin and one silver coin.
>
> Choose a box at random. From this box, withdraw one coin at random. If that happens to be a gold coin, then what is the probability that the next coin drawn from the same box is also a gold coin?
My thinking is this… Taking a box at random would be 33% for each box. Because you got one gold coin it cannot be the box with TWO silver coins, therefore the box must be either the gold and silver coin or the box with two gold coins. Each of which is equally likely so the chance of a second gold coin is 50%
I understand that this is a veridical paradox and that the answer is counter intuitive. But apparently the real answer is 66% !! I’m having a terrible time understanding how or why. Can anyone explain this like I was 5?
In: Mathematics
The GG box has a G1 and a G2 coin
The SS box has an S1 coin and an S2 coin
The GS box has a G3 coin and a S3 coin.
There are six scenarios (before we even choose a box):
1) We choose GG and then choose G1 followed by G2
2) We choose GG and then choose G2 followed by G1
3) We choose SS and then choose S1 followed by S2
4) We choose SS and then choose S2 followed by S1
5) We choose GS and then choose G3 followed by S3
6) We choose GS and then choose S3 followed by G3
We are in 1, 2, or 5. We don’t know which one. But 2 out of those 3 choices will yield a gold coin on our second pull.
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