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.)

Question

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

Answer 5

To find the probability that the Democratic candidate was elected given that a conservative judge was appointed to the Supreme Court, we can use Bayes' theorem.

Let's define the events:
A = Democratic candidate elected
B = Conservative judge appointed to Supreme Court

We are given:
P(A) = 2/3 (probability of Democratic candidate being elected)
P(¬A) = 1/3 (probability of Republican candidate being elected)
P(B|A) = 2/9 (probability of appointing a conservative judge if Democratic candidate is elected)
P(B|¬A) = 1/6 (probability of appointing a conservative judge if Republican candidate is elected)

We want to find P(A|B), the probability of the Democratic candidate being elected given that a conservative judge was appointed.

Using Bayes' theorem, we have:

P(A|B) = (P(B|A) * P(A)) / (P(B|A) * P(A) + P(B|¬A) * P(¬A))

Substituting the given probabilities:

P(A|B) = (2/9 * 2/3) / (2/9 * 2/3 + 1/6 * 1/3)

Simplifying the expression:

P(A|B) = (4/27) / (4/27 + 1/18)

P(A|B) = (4/27) / (8/54 + 3/54)

P(A|B) = (4/27) / (11/54)

P(A|B) = (4/27) * (54/11)

Calculating the result:

P(A|B) = 4/11 ≈ 0.364

Therefore, the probability that the Democratic candidate was elected given that a conservative judge was appointed to the Supreme Court is approximately 0.364, rounded to three decimal places.