A number of tourists roll up at the Humanist tearooms, all wanting tea. 21 of them don’t take milk. Twice as many want milk but not sugar as want neither; twice as many want both milk and sugar as want just sugar. But that’s not my probem. I just set the places. How many places should I set?
Each issue, we award a prize to three lucky winners – this time we have copies of the new collection of MR James' classic ghost stories, published by Oxford University Press. You can send us your answers (complete with your postal address, if you want to win) to editor[at]newhumanist.org.uk. Deadline is 1 October 2011. We will publish the solution alongside next issue's quiz.
Solution to the July/August 2011 quiz, "Come on, you've urn'ed it"
Imagine two equally likely alternative universes: one in which there is a white ball, W, in the urn, and one in which there is a black ball, B, in the urn.
The chairman of Ripoff Bank adds a white ball, w. In the first case he is equally likely to withdraw W as w; in the second he is equally likely to withdraw w as B; so to begin with the following are equally likely: he withdraws w leaving W; he withdraws W leaving w; he withdraws w leaving B; he withdraws B leaving w. Now let’s run the trial. Only the first 3 equally likely cases are compatible with fact.
Hence we have just three equally likely cases: he withdraws w leaving W; he withdraws W leaving w; he withdraws w leaving B; so it is twice as likely we are in a universe in which there was a white ball in the urn to begin with; so our chances of a morally unjustifiable and monstrous bonus are 2/3.
Since we are half as likely to have begun with a black ball in the urn, if the chairman returns his white ball to the urn our chances of a deferred bonus are those of the double whammy: wrong universe and picking the black ball from a white and a black. The chances of this are 1/3 X 1/2 = 1/6; so in this case the chances of a bonus: 1 – 1/6 = 5/6.
