A finite-stage, discrete-time, sequential decision theory problem is formulated. The problem is characterized by a sequence of decisions resulting in uncertain outcomes combined with a choice, between decisions, of experiment for obtaining information about previous outcomes. The solution to the problem entails finding optimal rules for the decisions and experiment choices by the method of backward induction. Three theorems are given which may be used to reduce the computational effort in some problem solutions. A measure of the conditional information in an experiment is defined and results are interpreted relative to that measure. Illustrative applications to a simple control problem are given.