Question

The probability of selecting an item in probability sampling, from the population is :

• A. Equal to zero
• B. Size of population
• C. Size of sample
• D. Between zero and one

Hint:

The key feature of probability sampling is that the selection probability is known and non-zero. Since it is a probability, it must lie in the range $(0, 1)$.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
By definition, in probability sampling, every element in the population has a known, non-zero probability of being selected in the sample.
Detailed Explanation:
Let us review the properties of probability:
- The probability $P(A)$ of any event $A$ must satisfy Axiom 1 of probability: \[ 0 \le P(A) \le 1 \] - In probability sampling, every item must have a positive, non-zero chance of selection to avoid selection bias (thus, $P > 0$).
- Since no single item is guaranteed to be selected in every sample (unless $n = N$, which is a census, not a sample), the probability of selecting any single item is strictly less than 1 (thus, $P < 1$).
- Therefore, the probability of selecting any specific item lies strictly between zero and one.

Step 2: Final Answer:
The probability is between zero and one, matching Option (D).