By Manin Yu. I.
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Extra resources for Honorary issue of Duke mathematical journal
This is the same as identifying the oldest child as the boy, and it changes the odds in a similar fashion. The most famous of all probability paradoxes is the St. Petersburg paradox, first set forth in a paper by the famous mathematician Daniel Bernoulli before the St. Petersburg Academy. Suppose I toss a penny and agree to pay you a dollar if it falls heads. If it comes tails, I toss again, this time paying you two dollars if the coin is heads. If it is tails again, I toss a third time and pay four dollars if it falls heads.
I t i s a sad commentary on the rise o f logic that it leads t o the decay of the art o f lying. E v e n among liars, the life of reason seems t o be gaining ground over the better life. W e refer to puzzle number 4 in the February issue, and i t s solution. I f w e accept the proposed solution, w e m u s t believe that liars can always be made the dupes o f their ozun principles, a situation, indeed, zuhich is bound to arise whenever lying takes the form o f slavish adherence to arbitrary rules.
The probability of a coincidence in each case (33 birth dates, 30 death dates) is close to 75 per cent. Sure enough, Polk and Harding were born on November 2, and three presidentsJefferson, Adams and Monroe- all died on July 4. Perhaps even more astounding is the paradox of the second ace. " The probability that you have a second ace can be calculated precisely. I t proves to be 5359/14498 which is less than 1/2. Suppose, however, that all of you agree upon a particular ace, say the Ace of Spades.