## Table Laplace Criterion

Strategy Expected Value

51 6G

52 53.3

### 53 43.3

The concept of expected value can also be combined with "probability" or "decision" trees to identify and quantify the potential risks. Another common term is the impact analysis diagram. Decision trees are used when a decision cannot be viewed as a single, isolated occurrence, but rather as a sequence of several interrelated decisions. In this case, the decision-maker makes an entire series of decisions simultaneously.

Consider the following problem. A product can be manufactured using Machine A or Machine B. Machine A has a 40 percent chance of being used and Machine B a 60 percent chance. Both machines use either Process C or D. When Machine A is selected, Process C is selected 80 percent of the time and Process D 20 percent. When Machine B is selected, Process C is selected 30 percent of the time and Process D 70 percent of the time. What is the probability of the product being produced by the various combinations?

Figure 17-3 shows the decision tree for this problem. The probability at the end of each branch (furthest to the right) is obtained by multiplying the branch probabilities together.