Bertrand's box paradox
Mathematical paradox / From Wikipedia, the free encyclopedia
Dear Wikiwand AI, let's keep it short by simply answering these key questions:
Can you list the top facts and stats about Bertrand's box paradox?
Summarize this article for a 10 year old
Bertrand's box paradox is a veridical paradox in elementary probability theory. It was first posed by Joseph Bertrand in his 1889 work Calcul des Probabilités.
![Thumb image](http://upload.wikimedia.org/wikipedia/commons/thumb/4/43/Three_mystery_boxes.jpg/640px-Three_mystery_boxes.jpg)
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?
A veridical paradox is a paradox whose correct solution seems to be counterintuitive. It may seem intuitive that the probability that the remaining coin is gold should be 1/2, but the probability is actually 2/3.[1] Bertrand showed that if 1/2 were correct, it would result in a contradiction, so 1/2 cannot be correct.
This simple but counterintuitive puzzle is used as a standard example in teaching probability theory. The solution illustrates some basic principles, including the Kolmogorov axioms.