### The German Tank Problem Revisited

I've written before about The German Tank Problem . Basically, it's a problem in which you try and estimate the number of tanks being produced by the enemy, based upon the serial numbers of the ones that were knocked out. This was a real problem from World War II, but is now often sold as the taxi problem, in case you are too sensitive to think about tanks. The moral of the story is that the spooks and spies were wrong, and the mathematicians right. Yay!!! I was happy with this until my post on this (which was almost a year ago). My ex-student, and Bayesian extraordinaire, Brendon Brewer , said something that bothered me. Namely, the chance of seeing a tank depends on the number of tanks, with more chance of seeing one if there are more of them (obviously!), and this seems to cancel out the effect of knowing the serial numbers of the tanks. So how could it work. I had a good week and so decided to return to the problem. Let's start you being a battlefield intellig