A person randomly chosen from a population has a probability of 25% of having a disease of hepatitis --- inflammation of the liver tissue. A medical test has been conducted to uncover the disease. This test is not 100% accurate. The probability that the test will show a positive result when the test is performed on the patient who has the disease is 0.64. Likewise, the probability that the test will show a positive result when the test is performed on the patient who does not have the disease is 0.35.

i)Draw a fully labelled tree diagram to represent the information given above.

ii)Calculate the probability that someone who is chosen randomly from the population and given the test for hepatitis will have a negative result (to 4 d.p.).

iii)A person selected randomly reacts negatively to the test. What is the probability that this person actually does not have the disease? (to 4 d.p.)?