Suppose that a certain mathematics class has 28 students. Of these, 14 are first-year students, 17 are business majors and 8 are neither.

a. Suppose that a business student is selected at random. What is the probability that he or she is also a first year student?

b. Suppose that student from this class is selected at random. Given that he or she is not a first-year student, what is the probability that he or she is a business major?


Let B = business major, F = 1st year . Then /B/ = 17, /F/ = 14, and U = set of all 28 students. So /U/ = 28. Then /B or F/ = 28 - 8 = 20 students. So draw a Venn diagram we have:

3 students are 1st year only.

11 students are both 1st year and business major.

6 students are business major only.

8 students are neither 1st year nor business major.

a. There are 14 first year students out of 28 students. so the probability is : 14/28 = 0.5

b. There are 14 student that are not first year students, and of these 6 are business major. So the probability is: 6/14 = 0.429.

  • $\begingroup$ Are you sure about a.? I thought a business student was being selected at random, which would make the answer 11/17. $\endgroup$ – Dalamar Mar 16 '14 at 20:42

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.