Consider three events, A,B, and C in a probability space. Let P(AB) = 0.2, P(AB) =...

 

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Consider three events, A,B, and C in a probability space. Let P(AB) = 0.2, P(AB) = 0.2, P(C) = 0.6, and P(ABC) = 0.15. It is known that A and B are independent, and that A and C are mutually exclusive. (a) Exploit the independence of A and B to fill in the probabilities for all events in a 2-event Karnaugh map involving events A and B. Show all your steps clearly. (b) Now use the fact that A and C are mutually exclusive to fill in the probabilities for all events in a 3-event Karnaugh map involving the events A, B, and C. Show your steps clearly. (c) Find the numerical value of P(AUBUC). Consider three events, A,B, and C in a probability space. Let P(AB) = 0.2, P(AB) = 0.2, P(C) = 0.6, and P(ABC) = 0.15. It is known that A and B are independent, and that A and C are mutually exclusive. (a) Exploit the independence of A and B to fill in the probabilities for all events in a 2-event Karnaugh map involving events A and B. Show all your steps clearly. (b) Now use the fact that A and C are mutually exclusive to fill in the probabilities for all events in a 3-event Karnaugh map involving the events A, B, and C. Show your steps clearly. (c) Find the numerical value of P(AUBUC).