Question

A university class has 27 students: 13 are history majors, 8 are accounting majors, and 6 are art majors. (Each student has only one of these majors.) The professor is planning to select two of the students for a demonstration. The first student will be selected at random, and then the second student will be selected at random from the remaining students. What is the probability that the first student selected is an accounting major and the second student is an art major?

Answer 1

8/27

Explanation:

There are a total of 27 students in the class, and 8 of them are accounting majors. Therefore, the probability of the first student selected being an accounting major is 8/27.

After the first student is selected, there will be 26 students remaining, out of which 6 are art majors. Therefore, the probability of the second student selected being an art major, given that the first student was an accounting major, is 6/26.

To find the probability of both events occurring together, we need to multiply the individual probabilities:

P(accounting major first) * P(art major second | accounting major first)

= (8/27) * (6/26)

= 48/702

= 8/117