Hypergeometric Distribution · Exercise 5

Suppose that a technology task force is being formed to study technology awareness among instructors. Assume that ten people will be randomly chosen to be on the committee from a group of 28 volunteers, 20 who are technically proficient and eight who are not. We are interested in the number on the committee who are not technically proficient.

(a) In words, define the random variable X.
(b) List the values that X may take on.
(c) How many instructors do you expect on the committee who are not technically proficient?
(d) Find the probability that at least five on the committee are not technically proficient.
(e) Find the probability that at most three on the committee are not technically proficient.

Its source prints no answer for this problem, so there's nothing to check against.

OpenStax, Introductory Business Statistics 2e · §4.1 Hypergeometric Distribution · Exercise 5