A state senate has 120 senators; 75 are democrats and 45 are republicans. Of the Democrats, 45 are liberal and 30 are conservative. Of the republicans, 30 are conservative and 15 are liberal, A.) Given that a senator is democrat, what is the probability that he or she is a liberal?  B.) Given that a senator is conservative, what is the probability that he or she is a republican?

A First Course in Probability (10th Edition)
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Chapter1: Combinatorial Analysis
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Use Baye's Theorem in solving the problem. Don't solve if not Baye's Theorem. Show all solutions.

A state senate has 120 senators; 75 are democrats and 45 are republicans. Of the Democrats, 45 are liberal and 30 are conservative. Of the republicans, 30 are conservative and 15 are liberal,

A.) Given that a senator is democrat, what is the probability that he or she is a liberal? 

B.) Given that a senator is conservative, what is the probability that he or she is a republican? 

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