Question

In a recent senatorial election, 59% of the voters in a certain district were registered as Democrats, 38% were registered as Republicans, and 3% were registered as Independents. The incumbent Democratic senator was reelected over her Republican and Independent opponents. Exit polls indicated that she gained 82% of the Democratic vote, 27% of the Republican vote, and 33% of the Independent vote. Assuming that the exit poll is accurate, what is the probability that a vote for the incumbent was cast by a registered Republican? (Round your answer to three decimal places.)

Answer 1

P(A) = 0.59

P(B) = 0.38

P(C) = 0.03

P(E|A) = 0.82

P(E|B) = 0.27

P(E|C) = 0.33

Required probability =

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