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18 February, 18:23

A population of voters contains 40% republicans and 60% democrats. it is reported that30% of the republicans and 70% of the democrats favor an election issue. a person chosenat random from this population is found to favor the issue in question. find the conditionalprobability that this person is a democrat

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  1. 18 February, 18:35
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    To get the probability of selecting a person who is a democrat and is favour to the issue, let us first calculate for the portions in each party who is favour on the issue.

    p (rep & favour) = 0.4 * 0.3 = 0.12

    p (dem & favour) = 0.6 * 0.7 = 0.42

    Therefore the total portions who are favour is:

    p (favour) = 0.12 + 0.42 = 0.54

    Hence the probability is:

    P (dem & favour) = 0.42 / 0.54 = 0.7778 = 0.78

    Therefore there is about 78% probability that the person selected who is favour to the issue is a democrat.
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