In a given? county, records show that of the registered? voters are50?% are? Dem

Question

In a given? county, records show that of the registered? voters are50?%

are? Democrats, 40?%

are? Republicans, and 10?%

are Independents. In an? election,

6060?%

of the? Democrats,

30%

of the? Republicans, and

90?%

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 an independent is

.....

The probability that the voter is a Democrat is

......

Explanation / Answer

Democrats = 0.50

Republcans = 0.40

Independents = 0.10

Voted for parks and recereation bond proposals:

60% of Democrats = 0.60 X 0.50 = 0.3

30% of Republicans = 0.30 X 0.40 = 0.12

90% of Independents = 0.90 X 0.10 = 0.09

The data is summarised in Table below:

                 Democrat      Republican            Independent            Total

Voted             0.30             0.12                      0.09                   0.51

Not voted        0.20              0.28                     0.01                   0.49

Total               0.50                0.40                  0.10                   1.00

(a) P(Republican/Voted) = P(Republican & Voted)/P(Voted) = 0.12/0.51 = 0.2353

(b) P(Independent/Voted) = P(Independent & voted)/P(Voted) = 0.09/0.51 = 0.1765

(c) P(Democrat/Voted) = P(Democrat & Voted)/P(Voted) = 0.3/0.51 = 0.5882

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