The Initial diagnosis of a patient's illness was potentially flu (F), cold(C), or hay fever (H), with probabilities 0.1, 0.2, and 0.7 respectively.A lab test wasthen given to the patient.Past tests on similar patients show the followingconditional probabilities on the test result being positive (+), neutral (0), ornegative (-) given that the patient is eventually determined to have F, C, or H:

P(+|F) = 0.7 P(0|F) = 0.2 P(-|F) = 0.1

P(+|C) = 0.1 P(0|C) = 0.8 P(-|C) = 0.1

P(+|H) = 0.1 P(0|H) = 0.3 P(-|H) = 0.6

Use Bayes Theorem to estimate the respective 9 conditional probabilities of F, C,and H given that a +, 0, or - test result has been observed.