2. (Bayes formula, Ns) In the setup of an assembly line, the system is either correctly or incorrectly adjusted. The probability of a correct adjustment is 0.95. When correctly adjusted, the system operates with a 2% defective rate. However, if incorrectly adjusted, it has a 50% defective rate. Assume that defects occur independently of each other. (1) (. conditional probabilities, where C (resp., I) represents the event that the system is correctly (resp., incorrectly) adjusted, and D (résp., N) represents the event that the next produced item is defective (resp., non-defective); Complete the tree diagram below by filling in the relevant probabilities and (2) ( r~) After the system starts a production run, what is the probability that a defect is observed? (Hint: D= (CN D) U (IND), Total Probability) (3) probability that the system is incorrectly adjusted? (Hint: P(I | D), Bayes Theorem) Suppose that one item selected by an inspector is found to be defective. What is the Items produced when correctly adiusted C N D I I Items produced when incorrectly adjusted

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