This chapter discusses the nature of probability statements in real-life situations before reviewing some basic probability concepts and relationships. It focuses on the processes by which probability judgements can be modified in the light of additional relevant information. The chapter also focuses on some of the more widely applicable and precise techniques for the ‘improvement’ of probability estimates, but it must be stressed that the ultimate criterion for the acceptability of any estimate is simply whether the decision maker in question is satisfied with it. An important distinction is necessary at the outset, between repeated sampling in situations where the probabilities of different outcomes remain constant or virtually constant and situations where the outcomes of earlier sampling affect the probabilities of different outcomes in subsequent samples. A company has for some time been conducting inspections of randomly chosen units of its finished product. The inspection results in an A or B grade being awarded to each item inspected.