> 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
Perhaps it would be easier to understand if you were to put a number on each coin.
Put the numbers G1 and G2 on the two gold coins that will be in the same box, S1 and S2 on the two silver coins in the same box, and G3 and S3 for the two remaining coins in the last box.
You’re equally likely to pick each box, and equally likely to pick each coin in the box. So, each coin has a 1/6 probability of being picked. Since we know that the coin you picked was golden, each of the golden coin still has the same probability, but as there’s only 3 more possibilities now, you only get 1/3. So, G3, the coin in the same box as the other silver coin, also only has 1/3 odds of being picked. And that’s the only possibility in which you draw a gold coin in the first one and a silver coin in the second one. So, the probability of drawing a gold coin twice is 1 – 1/3, or 2/3.
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