Medical studies have shown that 10 out of 100 adults comprise heart disease. When person with heart disease is given EKG test, a 0.9 probability exists that the test will be positive. When person with no heart disease is given an EKG test, 0.95 probabilities exists that the test will be negative. Assume that the person arrives at emergency room complaining of chest pains. An EKG test is given to this person.
1. If test is positive, what is the probability that this person really has heart disease?
2. If test is negative, what is probability that this person really does NOT have heart disease?
3. Assume the first EKG test is positive. In order to ensure, a second EKG test is given to person. What is the probability that this person has the heart disease if the second EKG test is as well positive?
4. Assume the first EKG test is positive. In order to ensure, a second EKG test is given to person. What is the probability that this person has heart disease if second EKG test is negative?