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Finite Math- help wanted. Super hard!

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In a past presidential election, it was estimated that the probability that the Republican candidate would be elected was 2/3, and therefore the probability that the Democratic candidate would be elected was 1/3 (the two Independent candidates were given no chance of being elected). It was also estimated that if the Republican candidate were elected, the probability that a conservative, moderate, or liberal judge would be appointed to the Supreme Court (one retirement was expected during the presidential term) was 1/3, 1/3, and 1/3, respectively. If the Democratic candidate were elected, the probabilities that a conservative, moderate, or liberal judge would be appointed to the Supreme Court would be 1/8, 1/4, and 5/8, respectively. A conservative judge was appointed to the Supreme Court during the presidential term. What is the probability that the Democratic candidate was elected? (Round your answer to three decimal places.)

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