Answer:
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
