Question

Giving a test to a group of students, the grades and if they were a business majors are summarized below. One student is chosen at random. Give your answer as a decimal out to at least 4 places.

	A	B	C	Total
Business Majors	5	18	2	25
Non-business Majors	12	10	8	30
Total	17	28	10	55

a) Find the probability that the student was a non-business major or got a grade of A.

____

b) Find the probability that the student was a non-business major and got a grade of A.

____

c) Find the probability that the student was a non-business major given they got a grade of A.

______

d) Find the probability that the student did not get a B grade.

______

e) Find P(B ∪∪ Business Major),

________

f) Find P(C | Business Major).

_______

Answer 1

(a) P(NBM or A) = P(NBM)+P(A) - P(NBM and A) = (30+17-12)/55 = 35/55 = 0.6364

(b) P(NBM and A) = 12/55 = 0.2181

(c) P(NBM|A) = P(NBM and A)/P(A) = 12/17 = 0.7059

(d) P(not B) = 1 - P(B) = 1 - (28/55) = 27/55 = 0.4909

(e) P(B or BM) = P(B)+P(BM)-P(B and BM) = (28+25-18)/55 = 35/55 = 0.6364

(f) P(C|BM) = P(C and BM)/P(BM) = 2/25 = 0.08