Question

L.1. 15 students respond to an online questionnaire. We sample 3 students at random one at a time without replacement to receive bookstore credit. Suppose that the 15 st udents consist of 5 s, 5 juniors, and 5 seniors. (a) Let the sample space S be the set of all Ordered triples of students in the order they were chosen. Let A be the event that "all three students in the sample have the same grade level". Let B be the event that "all three students have different grade levels". In each part count the given set (sample space or event). #S stands for size or cardinality of the set S. Show your work. (i) #S# ? (ii) #A-: ? (iii) #B- (b) Instead, take a differeut sample space U that consists of all Unordered samples, or 3 element sets of students, in which the order of the 3 students sanp11 des not matter. Let「C U be the event that tat least one sophomore is in the sample Find (i) # :

Answer 1

Sophomore = 5

Junior = 5

Senior = 5

A. Sample Space, S = No. of all ordered triplets

= Permutation(15,3) = P(15,3)

=2730

B. All three students in the sample have the same grade level, A = Combination_senior(5,3) + Combination_junior(5,3) + Combination_sophomore(5,3)

=3*Combination(5,3)

=3*C(5,3)

=30

C. All three students have different grades, B = Combination_senior(5,1) + Combination_junior(5,1) + Combination_sophomore(5,1)

=3*Combination(5,1)

=3*C(5,1)

=15

Note: Subscript signifies the group from which the selection has been made