In a past presidential election, it was estimated that the probability that the Republican candidate would be elected was 5/7, and therefore the probability that the Democratic candidate would be elected was 2/7 (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 1/7, 1/7, and 5/7, 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 1/3, 1/6, 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

The probability that the Democratic candidate was elected given that a conservative judge was appointed to the Supreme Court is .

Step-by-step explanation:

The conditional probability of an events A given that another events B has already occurred is given by:

The estimation of the past presidential election is provided.

Denote the events as follows:

R = a Republican candidate would be elected

D = a Democratic candidate would be elected

C = a conservative judge would be appointed to the Supreme Court

M = a moderate judge would be appointed to the Supreme Court

L = a liberal judge would be appointed to the Supreme Court

The information provided is:

It is provided that a conservative judge was appointed to the Supreme Court during the presidential term.

Compute the probability that the Democratic candidate was elected given that a conservative judge was appointed to the Supreme Court as follows:

Thus, the probability that the Democratic candidate was elected given that a conservative judge was appointed to the Supreme Court is .