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In a recent senatorial election, 47% of the voters in a certain district were registered as Democrats, 36% were registered as Republicans, and 17% 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, 22% of the Republican vote, and 26% 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

Apr 14, 2020

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47% of the voters were Democrats; she received 82% of this vote:      0,47 x 0.82  =  38.54%

36% of the voters were Republicans; she received 22% of this vote:    0.36 x 0.22  =     7.92%

17% of the voters were Independents; she recieved 26% of this vote:  0.17 x 0.26  =     4.42%

Adding these together, we see that she received 50.88% of the vote.

The Republican share was 7.92 / 50.88  =  15.57%.

Therefore, the probability that a vote for the incumbent is  0.1557.

Apr 14, 2020