Question

A classroom has ten students. Three students are freshman, two are sophomores, and five are juniors. Three students are randomly selected (without replacement) to participate in a survey. Consider the following events: A = Exactly 1 of the three selected is a freshman B = Exactly 2 of the three selected are juniors Find the following probability. If needed, round to FOUR decimal places. Pr(A∩B) = ___________

Answer 1

Answer:

0.25

Step-by-step explanation:

We have a total of ten student, and three students are randomly selected (without replacement) to participate in a survey. So, the total number of subsets of size 3 is given by 10C3=120.

On the other hand A=Exactly 1 of the three selected is a freshman. We have that three students are freshman in the classroom, we can form 3C1 different subsets of size 1 with the three freshman; besides B=Exactly 2 of the three selected are juniors, and five are juniors in the classroom. We can form 5C2 different subsets of size 2 with the five juniors. By the multiplication rule the number of different subsets of size 3 with exactly 1 freshman and 2 juniors is given by

(3C1)(5C2)=(3)(10)=30 and

Pr(A∩B)=30/120=0.25