Question

A change was proposed in the mathematics curriculum at a college. 70 mathematics majors were asked whether they approved of the proposed change. The results of the survey follow. Approved No opinion Did not approve

Female 21 6 12

Male 14 10 7

Suppose that a mathematics major is selected by chance. Find the probability that (a) The student is female, given no opinion. (b) The student approves of the proposed change. (c) The student is male, given the student does not approve of the proposed change. (d) The student is male and approves of the proposed change.

Answer 1

We have table as :

	Approved	No opinion	Did not approve	Total
Female	21	6	12	39
Male	14	10	7	31
Total	35	16	19	N= 70

a)

p ( female| no opinion )

= 0.375

b) The student approves of the proposed change.

p ( approve )

= 0.5

c) The student is male, given the student does not approve of the proposed change.

p ( male | did not approve )

= 0.37

d) The student is male and approves of the proposed change.

p ( male approved )

= 0.2