In a past presidential election, it was estimated that the probability that the Republican candidate would be elected was 1/5, and therefore the probability that the Democratic candidate would be elected was 4/5 (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 1/5, 1/5, and 3/5, 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 2/9, 1/3, and 4/9, 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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In a past presidential election, it was estimated that the probability that the Republican candidate would be elected was
1/5, and therefore the probability that the Democratic candidate would be elected was 4/5 (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 1/5, 1/5, and 3/5, 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 2/9, 1/3,
and 4/9, 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.)
Transcribed Image Text:In a past presidential election, it was estimated that the probability that the Republican candidate would be elected was 1/5, and therefore the probability that the Democratic candidate would be elected was 4/5 (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 1/5, 1/5, and 3/5, 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 2/9, 1/3, and 4/9, 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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