Summary

The probabilities of 2 mutually exclusive alternatives are combined by addition. Equivalent probabilities can be combined by averaging. Probabilities derived from 2 independent estimates of the same distribution of scores can be combined by Stouffer's Z method or by Fisher's chi squared method. Independent probabilities of the same event should be combined using the Bayes product of odds. The conjoint probability of 2 independent events with unknown outcomes is calculated by multiplication. There are 3 general approaches for dealing with problems with multiple uncertainties. Decision makers can ask an expert professional to give a judgment. They can follow conventional practices, or they can make a formal analysis like a decision analysis or cost-benefit analysis.

Combining probabilities

Table 2.1 lists 6 different methods of combining probabilities. Table 2.2 gives the numerical values when each method is used to combine a probability of .1 with probabilities ranging from .05 through .5. In the column headings of Table 2.2 the methods are numbered 1 through 6, from the method giving the highest combined probabilities on the left to the method giving the lowest combined probabilities on the right.