Question

If students can major either in Humanities or Sciences, which fact establishes that the observation "a student is male" is independent from the observation "a student is a Science major"?

A.	As many males major in Humanities as in Sciences.

B.	As many males as females major in Sciences.

C.	Males constitute the same fraction of students majoring in Humanities as in Sciences.

D.	The fraction of males among the students majoring in Humanities is equal to the fraction of females among the students majoring in Sciences.

Answer 1

There are only 2 majors in which the student can major: Science or humanities.

The two events: Student is male and that students is from science major would be independent if:

P( student is male | student is science major ) = P(student is male)

This is only possible if the proportion of male students is equal in both the science and the humanities stream because then the probability of a student being male given that he is from a science major would be same as the overall probability of the student being male. Therefore the fraction of males in humanities should be same as that in science major here. Therefore C is the correct answer here.