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 Democrat?
A) 0.55
B) 0.615
C) 0.45
D) 0.385

Question

Quizplus · Accepted Answer

To find the probability that someone who voted is a Democrat, use Bayes' rule: P(Democrat|Voted) = [P(Voted|Democrat) * P(Democrat)] / P(Voted). Calculate P(Voted) as the total probability of voting: 0.35*0.55 + 0.65*0.30 + 0.75*0.15 = 0.4875. Then, P(Democrat|Voted) = (0.35*0.55) / 0.4875 = 0.385.

Use Bayes' Rule to Find the Indicated Probability