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Mon 8 Sep, 2008 12:33 am
A bag contains a single ball, which is known to be either white or black (with equal probability). A white ball is put in, the bag is shaken, and a ball is then randomly removed. The removed ball happens to be white. What is now the probability that the bag currently contains a white ball?
Provide a convincing argument that your solution is correct.
2/3
And why is this kind of probability so confusing to so many people?
it's like Schrödinger's Cat
100% until you look at it.
Excluding Quantum Superposition, Robert is correct.
For the explanation, there are 3 possibilities:
1. The ball was black. A white was put in, and a white was taken out.
2. The ball was white. A white was put in, and the added one was taken out.
3. The ball was white. A white was put in, and the original one was taken out.
In 2 of the 3 possibilities, the original ball was white. 2/3.
In Quantum Theory, the original ball exists as both black and white at the same time. Only by observing it, does it choose one of the two states. However, once it is observed, the probability that it is white is still 2/3.
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