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18 February, 05:12

According to exit polls from the 2000 presidential election, the probability of a voter identifying as gay (including lesbians) was P (G) = 0.04. The probability of voting for Bush, given that a voter was gay, was P (B given G) = 0.25, and the probability of voting for Bush, given that a voter was not gay, was P (B given not G) = 0.50.

Find P (G intersection B)

Find P (G' intersection B) Find P (B), the overall probability of voting for Bush, keeping in mind that a voter was either gay and voted for Bush or not gay and voted for Bush.

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  1. 18 February, 05:32
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    P (G∩B) = 0.01

    P (G'∩B) = 0.48

    P (B) = 0.49

    Step-by-step explanation:

    The given probabilities are

    P (G) = 0.04

    P (B/G) = 0.25

    P (B/G') = 0.5

    P (G intersection B) = P (G∩B) = ?

    According to definition of conditional probability

    P (B/G) = P (G∩B) / P (G)

    So,

    P (G∩B) = P (G) * P (B/G)

    P (G∩B) = 0.04*0.25

    P (G∩B) = 0.01

    Thus, P (G intersection B) = P (G∩B) = 0.01.

    Now, P (G' intersection B) = P (G'∩B) = ?

    According to definition of conditional probability

    P (B/G') = P (G'∩B) / P (G')

    So,

    P (G'∩B) = P (G') * P (B/G')

    P (G') = 1-P (G) = 1-0.04=0.96

    P (G'∩B) = 0.96*0.5

    P (G'∩B) = 0.48

    Thus, P (G' intersection B) = P (G'∩B) = 0.48.

    Now, P (B) = ?

    We know a voter is either gay and voted for Bush or not gay and voted for Bush so,

    P (B) = P (G∩B) + P (G'∩B)

    P (B) = 0.01+0.48

    P (B) = 0.49

    Thus, the overall probability of voting for Bush P (B) = 0.49.
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