Schrödinger’s other box paradox Tony Mann University of Greenwich.

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Presentation transcript:

Schrödinger’s other box paradox Tony Mann University of Greenwich

You have choice of two boxes One contains x, the other 2x, for some unknown x All x equally probable Choose your box. Expected contents of the other box is ½ (x/2) + ½ (2x) = 5x/4 So you chose the wrong box You didn’t even have to open the box to know you’d made the wrong choice!

William Burnside’s example What is the probability that a random integer is divisible by 7? Well, here is a list of all the integers: {1, 7, 2, 14, 3, 21, 4, 28, 5, 35, 6, 42, 8, 49, 9, 56, 10, 63, 11, 70, 12, 77, …} So probability a random integer is divisible by 7 is obviously 1/2

Moral Before making your choice, find out exactly how the random number was chosen!