A population of voters contains 46% Republicans, 45% Democrats and the rest are Independents. Assume 50% of Republicans, 40% of Democrats, a

Question

A population of voters contains 46% Republicans, 45% Democrats and the rest are Independents. Assume 50% of Republicans, 40% of Democrats, and 60% of Independents favor an election issue. A person chosen at random from this population is found to favor the issue in question. Find the conditional probability this person is a democrat. (Round off up to two decimal points.) Group of answer choices 0.18 0.51 0.71 0.39

in progress 0
Đan Thu 2 months 2021-08-02T14:26:01+00:00 1 Answers 3 views 0

Answers ( )

    0
    2021-08-02T14:27:01+00:00

    Answer:

    The probability is 0.18

    Step-by-step explanation:

    Here, we are interested in calculating a conditional probability;

    Let the event that a voter is a Republican be R , the event that a voter is a Democrat be D and that a voter is an independent is I

    Let the event that the election issue is favored be F

    We have the following probabilities;

    P(R) = 46% = 0.46

    P(D) = 45% = 0.45

    P(I) = 1-0.45-0.46 = 0.09

    The conditional probability we want to calculate is;

    P(D | F) which can be read as probability of event D given event F

    From the question, we can identify the following conditional probabilities;

    P(F|R) = 0.46 * 0.5 = 0.23 (0.5 is gotten from 50% = 50/100)

    P(F | D) = 0.45 * 0.4 = 0.18

    P( F | I) = 0.09 * 0.6 = 0.054

    P(F) = 0.054 + 0.18 + 0.23 = 0.464

    Mathematically; From Baye’s theorem

    P( D | F) ={ P ( F | D) * P(D) }/ P(F)

    P( D | F) = (0.18 * 0.45)/0.464 = 0.1745

Leave an answer

Browse

Giải phương trình 1 ẩn: x + 2 - 2(x + 1) = -x . Hỏi x = ? ( )