The Role of the Frequency View of Probability in Solving the ``Problem of Three Prisoners''
Yuji Itoh (Keio University)
The "problem of three prisoners" is a very difficult probability problem.The purpose of this research is to identify the causes of the difficulty. Iconducted an experiment to see if the difficulty to apply subjects' "frequency view of probability" to the problem was one of the causes.
Subjects worked on two problems, the three-prisoner problem and the jewel problem. The latter had the similar mathematical structure to the former, but its content was expected to make it easy to apply the frequency view.
Some questions were asked to prompt subjects to apply the frequency view.
More subjects gave correct answer to the jewel problem than to the three-prisoner problem. Although neither hint questions nor experience to solve the jewel problem increased the correct answers to the three-prisoner problem, the experience with the jewel problem changed the error pattern.
The overall results show that the difficulty to apply the frequency view to the problem is one of the causes of the difficulty of three-prisoner problem.