[math] \newcommand{\NA}{{\rm NA}} \newcommand{\mat}[1]{{\bf#1}} \newcommand{\exref}[1]{\ref{##1}} \newcommand{\secstoprocess}{\all} \newcommand{\NA}{{\rm NA}} \newcommand{\mathds}{\mathbb}[/math]

Suppose we are attending a college which has 3000 students.

We wish to choose a subset of size 100 from the student body. Let [math]X[/math] represent the subset, chosen using the following possible strategies. For which strategies would it be appropriate to assign the uniform distribution to [math]X[/math]? If it is appropriate, what probability should we assign to each outcome?

• Take the first 100 students who enter the cafeteria to eat lunch.
• Ask the Registrar to sort the students by their Social Security number, and then take the first 100 in the resulting list.
• Ask the Registrar for a set of cards, with each card containing the name of exactly one student, and with each student appearing on exactly one card. Throw the cards out of a third-story window, then walk outside and pick up the first 100 cards that you find.