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22 May, 16:31

Of the entering class at a college, 75 % attended public high school, 15 % attended private high school, and 10 % were home schooled. Of those who attended public high school, 18 % made the Dean's list, 16 % of those who attended private high school made the Dean's list, and 17 % of those who were home schooled made the Dean's list. A student is randomly chosen. a) Find the probability that the student made the Dean's list. b) Find the probability that the student came from a public high school , given that the student made the Dean's list. c) Find the probability that the student was not home schooled , given that the student did not make the Dean's

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  1. 22 May, 20:00
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    a) - 0.7670

    b) - 0.176

    c) - 0.809

    Step-by-step explanation:

    Let us assume that,

    P (A) = Attended Public School

    =0.75

    P (B) = Attended Private School

    =0.15

    P (C) = Attended Home School

    =0.10

    P (E) = Student made the Dean's list

    Then,

    P (E/A) = Probability of Student made the Dean's list given that he/she attended Public School = 0.18

    P (E/B) = Probability of Student made the Dean's list given that he/she attended Private School = 0.16

    P (E/C) = Probability of Student made the Dean's list given that he/she is from Home School = 0.17

    a) - P (E) = Probability that Student made the Dean's List

    = P (A) * P (E/A) + P (B) * P (E/B) + P (C) * P (E/C)

    = 0.75 * 0.18 + 0.15 * 0.16 + 0.10 * 0.17

    = 0.176

    b) - P (A/E) = Probability that Student came from a Public high school , given that Student made the Dean's list

    = [ P (E/A) * P (A) ] : P (E)

    = [ 0.18 * 0.75 ] : 0.176

    = 0.767

    c) - P (C'/E') = Probability that Student was not home schooled , given that the Student did not make the Dean's list

    = [ P (E'/C') * P (C') ] : P (E')

    = [ 0.741 * 0.90 ] : 0.82 [∵P (E'/C') = P (A) * P (E'/A) + P (B) * P (E'/B)

    = 0.75 * 0.82 + 0.15 * 0.84

    = 0.741

    = 0.809
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