## Thursday, March 18, 2010

### Bertrand's Box

Suppose there are three cards:
• A black card that is black on both sides,
• A white card that is white on both sides, and
• A mixed card that is black on one side and white on the other.
All the cards are placed into a hat and one is pulled at random and placed on a table. The side facing up is black. What are the odds that the other side is also black?

1. 2/3. There are three black sides in the hat, each of which is equally likely to be placed facing up. Two of them have black on their reverse.

2. 50/50 I would say there are only two cards with black. There for pulling one car with black side up means there is either the option the other side is white or black, therefore 50/50.

3. I would say 1/2.
Since the side facing up is black in color, the side facing down can white or black.
Thus the probablity of the other side being Black is 1/2.

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4. The answer may be counter-intuitive, but I love questions like this. Take a look at the whole background and answer on wikipedia: http://en.wikipedia.org/wiki/Bertrand%27s_box_paradox

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