40. * In the United States, voters can be classied into one of three mutually ex

Question

40. * In the United States, voters can be classied into one of three mutually exclusive and collectively exhaustive groups: Democrats, Republicans, and Independents. In a large state, 50% of eligible voters are Democrats, 45% of eligible voters are Republicans, and 5% of eligible voters are Independents. The voter turnouts for the last election for the three groups are 40% of Democrats, 55% of Republicans, and 65% of Independents Given that a person did not vote in the last election, find the probability that the person is a Democrat.

Explanation / Answer

P(Democrat) = 0.50

P(Republicans) = 0.45

P(Independent) = 0.05

P(Vote| Democrat) = 0.40; so P(Did not vote| democrat) = 0.60

P(Vote| Republican) = 0.55; so P(Did not vote|Republican) = 0.45

P(Vote|Independent) = 0.65; so P(Did not vote| Independent) = 0.35

Hence,

P(Democrat| Did not vote)

= (0.60*0.50)/(0.60*0.50 + 0.45*0.45 + 0.35*0.05)

= 15/26

= 0.5769 [Rounded off to 4 decimal places]

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