In the context of probability, what does it mean when sampling is done without replacement?

• A. Each selected item is returned to the population before the next draw, so the total number of items remains the same.
• B. The probability of selecting any item remains constant for each draw.
• C. Each selected item is not returned to the population before the next draw, so the total number of items decreases with each selection.
• D. Sampling without replacement means that only one item can ever be selected.

Answer: (C)

Verified step by step guidance

1. Understand the concept of sampling in probability: it involves selecting items from a population to study or analyze.
2. Recognize that sampling can be done in two main ways: with replacement and without replacement.
3. Sampling with replacement means that after selecting an item, it is put back into the population before the next draw, so the population size remains constant and probabilities stay the same for each draw.
4. Sampling without replacement means that once an item is selected, it is not returned to the population, so the total number of items decreases with each selection, affecting the probabilities of subsequent draws.
5. Therefore, when sampling without replacement, the probability of selecting any particular item changes after each draw because the population size is reduced.