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