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

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