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?


1 Answer 1


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, 2014 at 20:42

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