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4. (6 pts) A brand A battery is in working condition with probability 0.8, whereas a brand B battery is in working condition with probability

4. (6 pts) A brand A battery is in working condition with probability 0.8, whereas a brand B battery is in working condition with probability 0.5. A battery is chosen from a bin consisting of 9 brand A and 11 brand B batteries. (a) What is the probability that the battery works? (b) Given that the battery does not work, what is the conditional probability that it was a type A battery

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