Use the information (and tree) from Example 3 to find the probability that a person chosen at random is healthy if the test is negative (a negative result indicates that the person does not have the disease).

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Suppose a test for diagnosing a certain serious disease is successful in detecting the disease in 95% of all persons infected but that it incorrectly diagnoses 4% of all healthy people as having the serious disease. Suppose also that it incorrectly diagnoses 12% of all people having another minor disease as having the serious disease. It is known that 2% of the population have the serious disease, 90% of the population are healthy, and 8% have the minor disease. Find the probability that a person selected at random has the serious disease if the test indicates that he or she does. Use H to represent healthy, M to represent having the minor disease, and D to represent having the serious disease.