Solve using R or R studio

1. With the monsoon season, we can have more cases of dengue fever, a mosquito-borne tropical disease caused by the dengue virus. Antibody tests are recommended during a dengue outbreak. However the presence of other viruses in the human body can have cross-reactive results yielding a high false positive rate. Assume a false positive rate of 10% and a false negative rate of 1%. (a) Given that a person has dengue, what is the probability of a positive test. (b) If one percent of a population has dengue, what fraction of the population will test positive. (c) If the individual tests positive, what is the probability that this individual has dengue? d) The public health department suggests aggressive screening so that half of those tested have dengue. In this case, what is the probability that an individual testing positive actually has dengue? (e) Given a proportion p of those tested having dengue, graph the probability that an individual testing positive actually has dengue. Indicate the values in parts (b) and (d)