Bunuel wrote:
In a certain large company, the ratio of college graduates with a graduate degree to non-college graduates is 1:8, and 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
Kudos for a correct solution.
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 :
24C : B = 2 : 3 = 16 :
24So, 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
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