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The prior probabilities for events A and Aare PA: ) = 0.45 and PA2 ) - 0.55. It is also known that PIA: A2 ) - 0. Suppose PCIAL) - 0.20 and P8A7) - 0.05. If needed, roun your answers to three decimal digits. (a) Are A, and Azmutually exclusive? Yes Explain your answer. O PA) PAIA) (5) PCA) PCA) - 1 (IM) PAI). PAIA) (iv) PANA) - 0 Option (lv) (b) Compute PIA; B) and PAO) PAN) - 0.08 PLAY B) - 0.0275 (c) Compute (8) PCB) - 0.1075 (d) Apply Bayes' theorem to compute PAJIB) and PA 18) PCA) - 0.7441 PA) 0.2558