The Solution, by the Method of Association, of Problems in Inverse Probability

Abstract

IN his review¹ of a book by Sir Arthur Eddington, Prof. Dingle criticises Sir Arthur's solution of a certain problem in inverse probability. Prof. Dingle proposes a second, simpler, and analogous, although different, problem: If A and D each speak the truth once in three times independently, and A says that D lies, what is the probability that D speaks the truth—He argues that from our knowledge of D, the probability is 1/3, while from our knowledge of A it is 2/3, and hence that neither for his problem nor for Eddington's can there be any consistent, correct solution. Yet Prof. Dingle's problem can be regarded as a problem in statistical association, and admits of one, and only one, solution.