Sixty percent of the student body at UTC is from the state of Tennessee (T), 30% percent are from other states (O), and the remainder are international students (I). Twenty percent of students from Tennessee live in the dormitories, whereas 50% of students from other states live in the dormitories. Finally, 80% of the international students live in the dormitories..
a.What percentage of UTC students live in the dormitories?
b.Given that a student lives in the dormitory, what is the probability that she/he is an international student?
c.Given that a student does not live in the dormitory, what is the probability that she/he is an international student?
2006-10-10 17:25:35 · 2 answers · asked by KISMET 2 in Science & Mathematics ➔ Mathematics
a. 20% of the 60% from TN, 50% of the 30% from other states, and 80% of the 10% international = 0.2*0.6 + 0.5*0.3 + 0.8*0.1 = 35%.
b. Use conditional probability: p(A | B) = p(A and B) / p(B)
In this case, A = "student is international", B = "student lives in the dorm".
p(A and B) = 0.8 * 0.1 = 0.08, and p(B) = 0.35.
c. Same idea, only this time, B = "student does not live in the dorm", and A = "student is international".
p(A and B) = same as before, p(B) = 1 - 0.35.
2006-10-10 17:59:20 · answer #1 · answered by James L 5 · 0⤊ 0⤋
A. (.6)(.2) = .12 (.3)(.5)= .15 (.1)(.8)= .18 added together you get .45 which is 45% of students of UTC
B. .18/.45 = .4 = 40/100
C. (.1)(.2) = .02 = 2/100
2006-10-10 18:02:41 · answer #2 · answered by the wise one 3 · 0⤊ 1⤋