A Microsoft Interview Question (aka basic Bayes' Theorem)

[Ed Miller]

If you don't know or understand Bayes' Theorem, this problem is for you. If you do, this problem will be trivial, and I ask you not to answer. Really, it isn't worth your time. [img]/images/graemlins/smile.gif[/img]

When I worked at Microsoft, I used to ask this as an interview question. Most of the candidates struggled with it. Hopefully you will figure it out quickly. Also, try to figure it out on your own before you read anyone else's answer.

You and a friend are playing Russian Roulette with a six-chambered revolver. You place two rounds in adjacent chambers and give the wheel a final spin. You hand the gun to your friend. He pulls the trigger...

Click. He hands the gun to you. You have a choice. You can spin it again, or you can simply shoot the next chamber. Does it matter which one you choose? If it does, why?