"Alright," says the commander gruffly. I try not to stare at the biscuits in his beard. "This week we've captured 5 German VX-Tanks, with serial numbers numbers 3, 5, 13, 22, and 27. They stopped producing the VX line years ago, although they're just now being deployed. The first tank they made had the serial number 1, the second tank, 2, and so on. All remaining VX tanks will be rolled out in the next battle. If they made 53 or more VX tanks, we'll lose the next battle, although if they only made 52 VX tanks - or if they made fewer than 52 - we'll win for sure. What're our chances?"

What's the probability England is going to win the next battle? In other words, what's the probability that the Germans produced 52 VX tanks or fewer?

  • 1
    $\begingroup$ That depends on the prior probability that the Germans produced N tanks for every N. Without that information, this question can't really be answered. $\endgroup$ – ffao May 13 '17 at 8:11
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    $\begingroup$ The German Tank Problem is not a puzzle but a standard mathematical problem. $\endgroup$ – Jaap Scherphuis May 13 '17 at 8:25
  • $\begingroup$ I had a nice time solving it on my own before going to the Wikipedia article, and I think other people could too. $\endgroup$ – J. Antonio Perez May 13 '17 at 8:34
  • $\begingroup$ Ffao, it is possible. If you assume that the prior probability of the Germans producing N tanks is the same for all possible N, then everything in the problem simplifies nicely. The answer is even rational $\endgroup$ – J. Antonio Perez May 13 '17 at 8:35
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    $\begingroup$ It can't be the same for all N, otherwise the sum of all probabilities would be infinite (and it needs to be 1). I checked and the Wikipedia page mentions this as well. $\endgroup$ – ffao May 13 '17 at 13:38

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