Question

Four students attempt to register online at the same time for an Introductory Statistics class that is full. Two are freshmen and two are sophomores. They are put on a wait list. Prior to the start of the semester, two enrolled students drop the course, so the professor decides to randomly select two of the four wait list students and gives them a seat in the class.

What is the probability that both students selected are freshmen?

(A) 1/12
(B) ¼
(C) ½
(D) ⅙

Answer 1

(A) 1/12

Explanation:

Since there are 4 students in the list and each of them has the same probability of being selected, the probability of selecting the first freshman is ¼ .

Once this student is selected, there are 3 students in the list, since again all of them have the same likelihood of being selected, the probability of choosing one more freshman is 1/3.

Since this fact does not depend on the previous choice, the events are independent, so the probability of choosing 2 freshmen is 1/4*1/3 = 1/12, and the right answer is (A)