There is a room with a machinegun and a guy with two dice. A person is taken into the room and the dice thrown. If they come up with two sixes then the person is shot. Otherwise he or she is let out and a group of ten people brought in. Again the dice are thrown and if they both come up sixes then the people are shot. Otherwise a group ten times bigger is brought into the room. This "game" goes on until a group is shot. (There is an infinite supply of people. Nobody goes into the room twice.) If you're taken into the room, what is the probability that you get out alive?
Argument 1. You are killed if two sixes are thrown. This happens 1 in 36 times. Therefore your chance of getting out alive is 35/36 = 97%. Argument 2. Most people who are taken into the room are killed, therefore you are very likely to die. For example, suppose the third batch are killed. Then 100 people who go into the room die and 11 survive. The chance of getting out alive is then 11/111 = 9.9%. (Working out the true probability is left as an exercise.) Which of these arguments is true? What's wrong with the other one? (You can make the situation even more extreme by making the probability a batch is shot even lower.) Rich GSV Matters Of Perspective
