a) A microscopic tuberculosis test is not completely accurate. The probability of a false positive (i.e. a positive result when the patient does not have TB) is 0.05. The probability of a false negative (i.e. a negative result when the patient has TB) is 0.1. Determine the probability that an individual will test positive if the prevalence of TB in the population is 30%.

b) A Tuberculosis test gives a positive result 95% of the time when the patient has Tuberculosis and a negative result 90% of the time when the patient does not have Tuberculosis. About 30% of the population has tuberculosis. If an individual tests positive, what is the probability that they have tuberculosis?