I am currently reading the sci-fi novel Manifold: Time by Stephen Baxter, which contains the following problem.
You are given a box which has either 10 marbles or 1000 marbles. By pressing a lever on the box, one marble is randomly taken out and given to you. You know that there is exactly one red marble.
After pressing the lever three times, you obtain a red marble. The book claims that this information implies, using Bayes' theorem, that the probability that there are 10 marbles in the box is 2/3.
Can anyone explain how this computation actually works out, or at least how one is supposed to set up Bayes' equation to get this answer? Thanks.