> 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
Here’s one way to see why it’s not 50-50
Suppose you have three boxes:
* a box containing 1,000,000 gold coins,
* a box containing 1,000,000 silver coins,
* a box containing 999,999 silver coins and 1 gold coin.
Choose a box at random. From this box, withdraw one coin from the 1,000,000 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?
If we follow your logic from earlier, you would say it can’t be the silver coin only box so it must be one of the other two boxes and your argument gives you 50%.
But it’s not 50% because the chance of you picking the gold coin in the box not all gold was literally 1 in a million: if you pick that box and randomly pick a coin it is almost certain to be silver. So you are overwhelmingly likely to have picked the gold only box if you see a gold coin. So the correct answer is 999,999 in a million not 50%.
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