In a certain large company, the ratio of college graduates with a graduate degree to non-college...

BTGmoderatorLU wrote: ↑

Tue May 26, 2020 6:14 am

Source: Magoosh

In a certain large company, the ratio of college graduates with a graduate degree to non-college graduates is 1:8, and the ratio of college graduates without a graduate degree to non-college graduates is 2:3. If one picks a random college graduate at this large company, what is the probability this college graduate has a graduate degree?

A. 1/11
B. 1/12
C. 1/13
D. 3/19
E. 3/43

The OA is D

It took me a while to see there are, indeed, 3 types of worker.
Let A = # of college graduates with a graduate degree
Let B = # of non-college graduates
Let C = # of college graduates without a graduate degree

Given: A : B = 1 : 8
Given: C : B = 2 : 3

Since both ratios share B, we need to create equivalent fractions that have the same value for B.
A : B = 1 : 8 = 3 : 24
C : B = 2 : 3 = 16 : 24

So, A : B : C = 3 : 24 : 16
3 + 24 + 16 = 43

So, for every 43 workers, there are:
- 3 college graduates with a graduate degree
- 24 non-college graduates
- 16 of college graduates without a graduate degree

If one picks a random college graduate at this large company, what is the probability this college graduate has a graduate degree?
We are picking a college graduate.
From the above info, we ignore the number of non-college graduates.
So, for every 19 college graduates, 3 have a graduate degree and 16 do not.

P(this college graduate has a graduate degree) = 3/19

Answer: D

Cheers,
Brent

BTGmoderatorLU wrote: ↑

Tue May 26, 2020 6:14 am

Source: Magoosh

In a certain large company, the ratio of college graduates with a graduate degree to non-college graduates is 1:8, and the ratio of college graduates without a graduate degree to non-college graduates is 2:3. If one picks a random college graduate at this large company, what is the probability this college graduate has a graduate degree?

A. 1/11
B. 1/12
C. 1/13
D. 3/19
E. 3/43

The OA is D

Solution:

We can let the number of non-college graduates be 24. Therefore, the number of college graduates with a graduate degree is 1/8 x 24 = 3, and the number of college graduates without a graduate degree 2/3 x 24 = 16. Therefore, there are 3 + 16 = 19 college graduates and the probability a randomly selected college graduate will have a graduate degree is 3/19.

Answer: D