In a past presidential election, it was estimated that the probability that the Republican candidate would be elected was 1/3, and therefore the probability that the Democratic candidate would be elected was 2/3 (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 1/6, 1/6, and 2/3, 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 2/9, 5/9, and 2/9, 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.)

Answer 1

Events:
R=Republican candidate elected
D=Democratic candidate elected
C=conservative judge appointed
M=moderate judge appointed
L=liberal judge appointed

P(R)=1/3
P(D)=1-1/3=2/3
P(C|R)=1/6
P(M|R)=1/6
P(L|R)=2/3
P(C|D)=2/9
P(M|D)=5/9
P(L|D)=2/9

Need to find P(D|C)
or probability of Democratic candidate elected given a conservative judge was elected.

Again, use total probability and then Bayes theorem.

Please attempt the problem, and post what you have.

Answer 2

i am unaware of what formula to use to solve this

Answer 3

It will be similar to the previous problem.
http://www.jiskha.com/display.cgi?id=1498184495

Answer 4

or the previous problem:
http://www.jiskha.com/display.cgi?id=1498438280