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Probability: Fallacies, Myths and Puzzles: Main Page

Why is every shuffled pack of cards a miracle


We have seen here how apparently 'likely' events are so improbable, but conversely truly incredible events happen all the time.

Take a pack of 52 cards. If the pack was well shuffled and you turned the cards over to reveal that they came out in this 'perfect' sequence:

cards


you would regard this as nothing short of a miracle. In fact, you would probably regard it as a life changing moment that you would recount to your grandchildren. Indeed, the probability that such an event would happen is 1 divided by 52! (that is 52 x 51 x 50 x 49 x ....x 3 x 2 x 1) because 52! is the total number of possible sequence of 52 playing cards. The number 52! is 

8065817517094390000000000000000000000000000000000000000000000000000

which is SUCH a big number that it is actually a bigger number than the number of atoms in the universe (see http://pages.prodigy.net/jhonig/bignum/indx.html for further information about big numbers).

So the probability of turning over exactly this 'perfect' sequence of cards is less than the probability of finding one specific atom in the entire universe. Yet, the probability of getting the (apparently random) sequence of cards that really is revealed is exactly the same as this tiny probability. So every sequence really is a miracle.


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Norman Fenton


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