BTGModeratorVI wrote: ↑Sat Jun 27, 2020 6:43 am
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%
Answer:
D
Solution:
We see that the problem is asking for the percentage of students who are male and non-finance majors. We can let the number of students at the lecture be 100. Thus, 30 students are finance majors and 70 are non-finance majors. Furthermore, 40 students are female, and 60 are male.
We can let x and y be the number of female and male students who are finance majors, respectively. So we can create the equations:
x + y = 30
and
x/y = (40 - x)/(60 - y)
Since y = 30 - x, we have:
x/(30 - x) = (40 - x)/(60 - (30 - x))
x/(30 - x) = (40 - x)/(30 + x)
x(30 + x) = (30 - x)(40 - x)
30x + x^2 = 1200 - 70x + x^2
100x = 1200
x = 12
So we have 12 female finance majors, which means there are 30 - 12 = 18 male finance majors, and therefore, there are 60 - 18 = 42 male students who are not finance majors.
Alternate Solution:
We see that the problem is asking for the percentage of students who are male and non-finance majors. We can let the number of students at the lecture be 100. Thus 30 students are finance majors and 70 are non-finance majors. Furthermore, 40 students are female and 60 are male.
Since the gender distribution is the same for both finance and non-finance majors is the same, 40% of both finance and non-finance majors is female and 60% of both finance and non-finance majors is male. Thus, of the 70 non-finance majors, 70*(0.6) = 42 are male. Since we assumed that there were 100 students in the class, the probability that a randomly chosen student turns out to be a non-finance major male is 42/100 = 42%.
Answer: D
