A state senate has120 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 15are 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? Round off your final answer to five decimal places

A First Course in Probability (10th Edition)
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Chapter1: Combinatorial Analysis
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(Use Baye's Theorem)

A state senate has120 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 15are 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?

Round off your final answer to five decimal places

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