A rare disease affects 2% of the population. A test has a sensitivity of 97%, i.e., it will give a positive result 97% of the time that a person actually has the disease. The same test also has a specificity of 99%, i.e., it will give a negative result 99% of the time when a person does not have the disease. Denote the event that a randomly selected person has a disease by D, and the event that a randomly selected person has a positive blood test by T.

a)Express the given information in probability notation.

b)Calculate the probability that a randomly selected person has a positive blood test.

c)Calculate the probability that a randomly selected person has the disease, given that they have a positive blood test.