3.3 Sampling from a small population

Sampling without replacement (i.e. no case can be sampled twice) means we no longer have independence. Example: Imagine there are 10 students in a class, including you. The probability of you being picked for a question is 1/10. If the teacher asks 3 questions and doesn’t ask the same person twice, what is the probability that you will not be picked?

9/10 * 8/9 * 7/8 = 0.7

There is a 70% chance you won’t get picked.

Interestingly, when sampling a small fraction of the total population (under 10%), observations are nearly independent, even when sampling without replacement.