Q2. a. State and prove Bayes law of probability. b. A patient is thought to have...

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Q2. a. State and prove Bayes law of probability. b. A patient is thought to have one of the three diseases, A1 A2 and A3 whose probabilities under given conditions are 1/2, 1/6/ 1/3 respectively. A test is carried out to diagnosis and yields a positive result with a probability of 0.1 for A1, a probability of 0.2 for A2, and a probability of 0.9 for A3. A test is conducted and found positive. Use Bayes of probability, and revise the possibility of A1 after (CLO-2) (10,10-points) testing. dom unriable y as given below. Q2. a. State and prove Bayes law of probability. b. A patient is thought to have one of the three diseases, A1 A2 and A3 whose probabilities under given conditions are 1/2, 1/6/ 1/3 respectively. A test is carried out to diagnosis and yields a positive result with a probability of 0.1 for A1, a probability of 0.2 for A2, and a probability of 0.9 for A3. A test is conducted and found positive. Use Bayes of probability, and revise the possibility of A1 after (CLO-2) (10,10-points) testing. dom unriable y as given below.