BTGmoderatorDC wrote:In a given finance lecture, 30% of the students are finance majors, and 40% of the students are female. The gender distribution for finance majors and non-finance majors is the same. If one student is called on at random, what is the probability that the student is neither female nor a finance major?
A. 70%
B. 60%
C. 58%
D. 42%
E. 30%
The gender distribution for ALL the students = 40% female, 60% male.
For the gender distribution for finance majors and non-finance majors to be the same:
Finance majors = 40% female, 60% male.
Non-finance majors = 40% female, 60% male.
(If the gender distribution is ANY OTHER RATIO -- if both types of majors are 30% female, 70% male, for example -- then the gender distribution for all the students will NOT be 40% female, 60% male.)
We can use the following formula for overlapping groups:
Total = Group 1 + Group 2 - Both + Neither.
The big idea with overlapping groups is to SUBTRACT THE OVERLAP.
When we count everyone in Group 1 (finance students) and everyone in Group 2 (females), those who are in BOTH groups (female finance students) get counted twice.
So that we don't double-count those who are in both groups, we SUBTRACT THE OVERLAP from the total.
In the problem at hand:
Let the total = 100.
Group 1 = finance majors = 30.
Group 2 = females = 40.
Since 40% of the finance majors are female, BOTH female and a finance major = .4(30) = 12.
Let N = the number of students who are NEITHER female NOR a finance major.
Plugging these values into the equation above, we get:
100 = 30 + 40 - 12 + N
N = 42.
Thus, P(neither female nor a finance major) = 42/100 = 42%.
The correct answer is
D.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at
[email protected].
Student Review #1
Student Review #2
Student Review #3
