2) 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?

Step-by-step explanation: Given that 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.

We are to find the probability that the college graduate has a graduate degree, if one picks a random college graduate at this large company.

According to the given information, we have

the ratio of college graduates with a graduate degree to non-college graduates is

[tex]a:b=1:8=3\times1:3\times8=3:24[/tex]

and the ratio of college graduates without a graduate degree to non-college graduates is

[tex]c:b=2:3=2\times8:3\times8=16:24.[/tex]

Therefore, the ratio of college graduates with a graduate degree to the college graduates without a graduate degree to non-college graduates is

[tex]a:c:b=3:16:24.[/tex]

So, the probability that the college graduate has a graduate degree, if one picks a random college graduate at this large company is

[tex]\dfrac{a}{a+b+c}=\dfrac{3}{3+16+24}=\dfrac{3}{43}=0.07.[/tex]

Thus, the required probability is 0.07.