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Revising Probabilities 547

is simply (.5)(280,000) (.5)(0) $140,000. Remembering that the expected

profit without the test is $120,000, we find the test has an EVI of 140,000 

120,000 $20,000. This test is much less valuable than the perfect seismic test

examined earlier. Nonetheless, if the test is inexpensive enough (costs less than

$20,000), the partners should elect it.

REVISING PROBABILITIES

In many situations, the decision maker possesses potentially valuable informa-

tion, but in a form that is not readily usable. Typically, the decision maker must

ask: How does this piece of information alter my assessment of an uncertain

event? Does it make the event more or less likely? By how much should I revise

the event’s probability? A considerable body of research has studied the ways

in which individuals make probabilistic predictions. The overwhelming evi-

dence from these studies is that one’s intuition often is a poor guide when it

comes to probability assessment and revision. (See the discussion of intuitive

prediction later in the chapter.) Fortunately, some basic results in probability

provide a formal method for handling this task.

To illustrate the method, suppose the partners lack the seismic record

listed in Table 13.1. Instead, they have the following summary information

about the accuracy of the seismic test. The vendor of the test certifies that, in

the past, sites that were actually wet tested “good” three-quarters of the time and

dry sites tested “bad” two-thirds of the time. In mathematical terms, we have

Pr(GƒW) 3/4 and Pr(BƒD) 2/3. As before, the partners assess a 40 percent

chance that the site is wet based on their information prior to the seismic test,

Pr(W)  .4.

How can the partners derive Pr(WƒG) and Pr(WƒB), the two key proba-

bilities they need to solve their decision tree? The most direct way is to com-

pute the table of joint probabilities in Table 13.1. Consider the calculation of

one such joint probability, Pr(W&G), appearing in the upper-left corner of

the table. The partners reason as follows: According to their prior judgment,

the site is wet 40 percent of the time. A wet site can be expected to test good

three-quarters of the time. Therefore, the site is both wet and good three-

quarters of 40 percent of the time, or 30 percent of the time. In algebraic

terms, we have Pr(W&G) (3/4)(.4)  .3. What is the probability that the site

is dry and (falsely) tests good? Since Pr(D)  .6 and only one-third of dry sites

test good, the joint probability is Pr(D&G) (1/3)(.6)  .2. The other joint

probabilities are computed in similar fashion. The basic result is that any joint

probability can be expressed as the product of a prior probability and a con-

ditional probability. In the first calculation, we made use of the result

Pr(W&G)Pr(GƒW)Pr(W). [13.1]

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