Wednesday, June 21, 2006

The Game Show

The Game Show puzzle has bewildered some of the greatest mathematicians. It's solution was so counter-intuitive that it was not accepted by the academic community for quite some time. See if you can get your head around it:

You are on a game show. In front of you are three boxes, one of which contains the keys to a brand new Porsche. If you pick the box with the keys, the car is yours. The game show host gets you to point to one of the three boxes. Now, before checking the box you have chosen, the game show host removes one of the other two boxes, and this is a box which does not contain the keys. So, if you choose box A, then the host will remove either box B or box C, depending on which box does not contain the keys. If the keys are in box A, then the host will remove either B or C - it does not matter which.

Now comes the dilemma. After the host has removed a box, should you change your decision? Does this increase your chances of winning the car?

People well-learned in probability would instinctively claim that it doesn't matter whether you change your decision or not: the probability of choosing the keys is always 1/3. But this is in fact false. You actually increase your chances of winning if you change your decision. The probability of choosing goes from 1/3 to 2/3.

But why? The probabilities for all the boxes should be 1/3. Well, probabilities are not concrete properties of objects - they change with situations. After the host removes a box, he has given you a new piece of information. Before he takes it away, the probability that the keys were in one of the two boxes which you did not choose was 2/3. So when he removes the box, the probability that it is in the box that he does not take away becomes 2/3. So there you have it - logic works in funny ways.


me again said...

is the probabilities changing to the situation, bayesian probability theorem?

Anonymous said...

ancient greek meaning of life

Religious and spiritual find perfect love and a complete expression of one's humanness in a relationship with God achieve a supernatural connection within the natural context achieve enlightenment and inner peace become like God, or divine glorify God experience personal justice (i.e. to be rewarded for goodness) experience existence from an infinite number of perspectives in order to expand the consciousness of all there is (i.e. to seek objectivity) be a filter of creation between heaven and hell

Anonymous said...


Entrepreneurial model: founders of religions act like entrepreneurs, developing new products (religions) to sell to consumers (to convert people to). According to this model, most founders of new religions already have experience in several religious groups before they begin their own. They take ideas from the pre-existing religions, and try to improve on them to make them more popular.

Anonymous said...

Determinism in quantum mechanics

DIVINE MIND is the one and only reality. When we incorporate the ideas that form this Mind into our mind and persevere in those ideas, a mighty strength wells up within us. Then we have a foundation for the spiritual body, the body not made with hands, eternal in the heavens. When the spiritual body is established in consciousness, its strength and power is transmitted to the visible body and to all the things that we touch in the world about us.

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