EXAMPLE 9 Arsenic Testing: Conditional Probability Models

Using the information on testing for arsenic given in Example 8, we construct a model for the conditional probability of possible test results given the water contains arsenic.

From information about the test, we know that . Using the complement rule (Rule 3) gives the probability of a false negative:

Fortunately, this probability is quite low! Table 8.4 gives the model for the conditional probability of the test results given the water sample contains arsenic.