The crucial step in your argumentation is from A to B. Here you are changing your a-priori probabilities. Counterintuitively, the probability of dying is not 1⁄2.
This paradox is known as the Monty Hall Problem: http://en.wikipedia.org/wiki/Monty_Hall_problem
The crucial step in your argumentation is from A to B. Here you are changing your a-priori probabilities. Counterintuitively, the probability of dying is not 1⁄2.
This paradox is known as the Monty Hall Problem: http://en.wikipedia.org/wiki/Monty_Hall_problem