Question: SELECTION OF SUPREME COURT JUDGES In a past presidential election, it was estimated that the probability that the Republican candidate would be elected was , and therefore the probability that the Democratic candidate would be elected was (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 , , and , 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 , , and , respectively. A conservative judge was appointed to the Supreme Court during the presidential term. What is the probability that the Democratic candidate was elected?