---
title: "Quiz: a tea-time teaser"
date: "2011-09-22T13:00:45+01:00"
modified: "2011-09-22T13:00:45+01:00"
url: "https://newhumanist.org.uk/articles/quiz-a-tea-time-teaser/"
post_id: 5469
---

# Quiz: a tea-time teaser

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](/articles/2663/book-review-collected-ghost-stories-by-mr-james), 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”](/articles/2636/quiz-come-on-youve-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.