Use Bayes' rule to find the indicated probability:
-In Cumberland County, 55% of registered voters are Democrats, 30% are Republicans and 15% are independent. During a recent election, 35% of the Democrats voted, 65% of the Republicans voted, and 75% of the independent voted. What is the probability that someone who voted is a Republican?
A) 0.225
B) 0.39
C) 0.065
D) 0.385

Question

Quizplus · Accepted Answer

To find the probability that someone who voted is a Republican, we use Bayes' rule. First, calculate the total probability of voting, which is the sum of the probabilities of each group voting:- Democrats: 55% * 35% = 19.25%- Republicans: 30% * 65% = 19.5%- Independents: 15% * 75% = 11.25%Total probability of voting = 19.25% + 19.5% + 11.25% = 50%Now, the probability that a voter is a Republican is the proportion of Republican voters in the total voting population:Probability(Republican | Voted) = (Probability(Republican) * Probability(Voted | Republican)) / Total probability of voting = (30% * 65%) / 50% = 19.5% / 50% = 0.39.

Use Bayes' Rule to Find the Indicated Probability