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 was then taken from the patient. Past tests on similar patients show the following conditional probabilities on the test result being positive (+), neutral (0), or negative (-): 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 the Bayes Theorem to estimate the respective probabilities of F, C, and H given that a +, 0, or - test result has been observed.