Question

A Corporation receives 120 applications for positions from recent college graduates in POLS. Assume that 40% of these applicants are graduated from MIT. If they randomly select two application. What is the probability that one of them is MIT graduate?

Answer 1

Solution:

There are 120 applications.

Given that 40% of the applicants are MIT graduates.

Hence, total number of applicants who are MIT graduate = 120×(40/100) = 48

Hence, total number of applicants who are not MIT graduate = 120 - 48 = 72

Now we have randomly selected 2 applications and we want to find the probability that one of them is MIT graduate.

Only one of the selected 2 applicants will be MIT graduate if one of them is selected from 48 MIT graduates and one of them is selected from 72 non MIT graduates.

Total number of ways of selecting one MIT graduate from 48 MIT graduates is,

Total number of ways of selecting one non MIT graduate from 72 non MIT graduates is,

Total number of ways of selecting 2 applications from 120 applications is,

Hence, probability that one of them is MIT graduate is,

P = (48 × 72)/7140 = 0.4840

Hence, the probability that one of them is MIT graduate is 0.4840.