SELECTION OF SUPREME COURT JUDGES In a past presidential election, it was estimated that the probability that the Republican candidate would be elected was
3
5
and therefore the probability that the Democratic candidate would be elected was
2
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
2
,
1
3
, and
1
6
, 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
,
3
8
, and
1
2
, respectively. A conservative judge was appointed to the Supreme Court during the presidential term. What is the probability that the Democratic candidate was elected?