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De Gruyter Advent Calendar | Door 2

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Is there anyone alive who isn't familiar with Alice in Wonderland? If they haven't read the book by Lewis Carroll, the majority have at least seen one of the numerous film adaptations of the strange story in which Alice follows the White Rabbit into an outlandish world.

Much less well known, however, is that Lewis Carroll was in fact a pseudonym for the mathematician Charles Lutwidge Dodgson. Today's entry presents you one of Dodgson's familiar stochastic problems.


Sleepless nights
Dodgson, better known under the pseudonym Lewis Carroll, published 72 mathematical problems and their solutions in 1893 under the title Pillow-Problems thought out during sleepless nights. About them, he writes: Nearly all […] having been solved in the head, while laying awake at night.

It's your turn!
For door number 2, we have selected a problem with a solution that is both ingenious and descriptive of stochastic methodology.

A bag contains a counter that can be either white or black. A white counter is now also placed in the bag. The bag is shaken vigorously and a counter is withdrawn from it that turns out to be white. What is the probability of the counter still in the bag also being white?

a) 1/2
b) 1/3
c) 2/3 

CoverThe puzzle is taken from the German publication Berühmte Aufgaben der Stochastik. If you want to know the right answer to the question, click here.