A certain virus infects 3% of a population. A test has been developed to detect the virus in a person. A person tests positive 94% of the time if the person has the virus ( i.e., 94% sensitivity) and negative 92% of time if the person does not have the virus (i.e., 92% specificity). Assume that a person is chosen randomly from the population to take a test. The probability tree for the question is given below.

Virus Test P( V and + ) = 0.0282 0.94 V 0.03 0.06 P( V and - ) = 0.0018 O P( V and + ) = 0.0776 0.97 0.08 0.92 P( V and - ) = 0.8924 Q a) Find the probability of a false positive, P( + | V) - b) If a randomly selected person from the community tests positive, what is the probability that the person does not have the virus? (Round your final answer to 4 decimal places.) P(V + )