> 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
Label all the coins.
Box one contains gold coins G1 and G2. Box two contains silver coins S1 and S2. Box three contains coins G3 and S3 (which are gold and silver, respectively).
Pick a box at random, then randomly draw a coin. The possible options for the coins you get are:
– G1, and then the next coin must be G2.
– G2, and the next coin must be G1.
– S1, and the next coin must be S2.
– S2, and the next coin must be S1.
– G3, and the next coin must be S3.
– S3, and the next coin must be G3.
So if you draw a gold coin, you know your second coin must be G1, G2, or S3. Two of these three outcomes mean you have the double coin box. 66%.
Latest Answers