In a given county, records show that of the registered voters, 45% are Democrats

Question

In a given county, records show that of the registered voters, 45% are Democrats, 35% are Republicans, and 20% are Independents. In an election, 60% of the Democrats, 20% of the Republicans, and 80% of the Independents voted in favor of a parks and recreation bond proposal. If a registered voter chosen at random is found to have voted in favor of the bond, what is the probability that the voter is a Republican? An Independent? A Democrat?

The probability that the voter is a Republican is

The probability that the voter is a Independent is

The probability that the voter is a Democrat is

Explanation / Answer

P(Democrats) = 0.45

P(Republicans) = 0.35

P(Independents) = 0.20

P(favor of the bond) = 0.45*(0.6)+0.35*(0.20)+0.20*(0.8) = 0.5

The probability that the voter is a Republican is If a registered voter chosen at random is found to have voted in favor of the bond = 0.35*(0.20) /0.5= 0.07/0.5 = 0.14

The probability that the voter is a Independent is If a registered voter chosen at random is found to have voted in favor of the bond = 0.20*(0.8) /0.5 = 0.16/0.5 = 0.32

The probability that the voter is a Democrat is If a registered voter chosen at random is found to have voted in favor of the bond = 0.45*(0.6)/0.5 = 0.54

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