A disease is known to be present in 2.5% of the population. A new test is developed to help determine whether someone has the disease. If a person has the disease, then the test will be positive 95% of the time. If the person does not have the disease the test will be positive 2% of the time. a) Draw a tree diagram to represent this information. b) A person is selected at random from the population and tested for the disease. Calculate the probability that the test is positive. c) A doctor selects a person at random from the population and performs the test. Given that the test is positive calculate the probability that the person does not have the disease. d) Comment on the usefulness of this new test for the disease