# Question 6. [Karnaugh Puzzle) Consider three events, A,B, and C in a probability space. Let P(AB) = 0.25, P(ABC) = 0.25, P(C) = 0.2, and P(ABC) = 0.1. 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 Care 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(AU BUC).

KMLNZC The Asker · Probability and Statistics

Transcribed Image Text: 6. [Karnaugh Puzzle) Consider three events, A,B, and C in a probability space. Let P(AB) = 0.25, P(ABC) = 0.25, P(C) = 0.2, and P(ABC) = 0.1. 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 Care 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(AU BUC).
More
Transcribed Image Text: 6. [Karnaugh Puzzle) Consider three events, A,B, and C in a probability space. Let P(AB) = 0.25, P(ABC) = 0.25, P(C) = 0.2, and P(ABC) = 0.1. 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 Care 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(AU BUC).