(a)You enter a tournament where there are only three types of players (excellent, good and regular). Your probability of winning a game against excellent players is 0.3, 0.4 against good players and 0.5 against standard players. You play a game against a randomly chose opponent. What is you probability of winning? (b)Suppose that two defective refrigerators have been included in a shipment of six refrigerators. The buyer begins to test the six refrigerators one at a time. Let D denote the outcome that the refrigerator is defective and G the outcome that it is good. What is the probability that the inspection of the first four refrigerators resulted in the ordered sequence DGGD?

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(a)You enter a tournament where there are only three types of players (excellent, good and regular). Your probability of winning a game against excellent players is 0.3, 0.4 against good players and 0.5 against standard players. You play a game against a randomly chose opponent. What is you probability of winning?

(b)Suppose that two defective refrigerators have been included in a shipment of six refrigerators. The buyer begins to test the six refrigerators one at a time. Let D denote the outcome that the refrigerator is defective and G the outcome that it is good. What is the probability that the inspection of the first four refrigerators resulted in the ordered sequence DGGD?

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