In a certain large company, the ratio of college graduates with a graduate

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?

First we combine the two statements to form 1 ratio of 3 terms.
The common term in both the statements is non-college graduates so we use that to combine.
The lcm of 8 and 3 is 24.
The first ratio can be written as 3:24
The second ratio can be written as 16:24
The combines ration is
college gradauate with a college degree : non-college graduates : college graduates without a college degree
3:24:16

We want the probability that a randomly selected college graduate has a graduate degree. That is equal to:


$$\frac{3}{3+24+16}=\frac{3}{43}$$