Medical studies have shown that 10 out of 100 adults have heart disease. When a person with heart disease is given an EKG test, a 0.9 probability exists that the test will be positive. When a person without heart disease is given an EKG test, a 0.95 probability exists that the test will be negative. Suppose that a person arrives at an emergency room complaining of chest pains. An EKG test is given to this person.
1. If the test is positive, what is the probability that this person actually has heart disease?
2. If the test is negative, what is the probability that this person actually does NOT have heart disease?
3. Suppose the first EKG test is positive. In order to make sure, a second EKG test is given to the person. What is the probability that this person has heart disease if the second EKG test is also positive?
4. Suppose the first EKG test is positive. In order to make sure, a second EKG test is given to the person. What is the probability that this person has heart disease if the second EKG test is negative?