Question

Suppose that there are three different sessions in STAT 221, with exactly 10 students

in each session. In the first session, there are 9 sophomores, in the second session there are 4 sophomores, and in the third session, there are 7 sophomores. In each session, a group of 3 students is randomly selected for a team project. What is the expected number of sessions in which the selected group of 3 will consist entirely of sophomores?​

Answer 1

The expected number of sessions in which the selected group of 3 will consist entirely of sophomores = 1.025

Explanation:

In the first session, there are 10 students and 9 sophomores.

Probability of a selected group of 3 consisting entirely of sophomores = (9/10) × (8/9) × (7/8) = (7/10) = 0.70

In the second session, there are 10 students with 4 sophomores

Probability of a selected group of 3 consisting entirely of sophomores = (4/10) × (3/9) × (2/8) = (1/30) = 0.03333

In the third session, there are 10 students with 7 sophomores

Probability of a selected group of 3 consisting entirely of sophomores = (7/10) × (6/9) × (5/8) = (7/24) = 0.2916666667

Expected value is given as

E(X) = Σ xᵢpᵢ

xᵢ = each variable or each session

pᵢ = Probability of a selected group of 3 consisting entirely of sophomores in each session

E(X) = [1 × (7/10)] + [1 × (1/30)] + [1 × (7/24)]

= 1.025

Hope this Helps!!!