Step 1: Understanding the Question
The question asks for the probability that a specific, pre-determined unit from a population of size \(N\) is selected at the second draw, given the sampling method is Simple Random Sampling Without Replacement (SRSWOR).
Step 2: Key Formula or Approach
In SRSWOR, the probability of any specific unit being selected is the same for every draw. We can prove this using conditional probability. For a specific unit to be selected at the second draw, it must not have been selected at the first draw.
\[P(\text{Unit selected at 2nd draw}) \] \[= P(\text{Unit not selected at 1st draw}) \times P(\text{Unit selected at 2nd draw} | \text{Not selected at 1st})\]
Step 3: Detailed Explanation
Let the population size be \(N\). We want to find the probability of selecting a specific unit, say unit \(U_i\), at the second draw.
The probability of not selecting unit \(U_i\) in the first draw is \( \frac{N-1}{N} \), since there are \(N-1\) other units that could be chosen out of \(N\).
After the first draw (where \(U_i\) was not selected), there are \(N-1\) units remaining in the population.
The probability of selecting unit \(U_i\) in the second draw, given it was not selected in the first, is \( \frac{1}{N-1} \).
Combining these, the overall probability is:
\[
P(\text{select } U_i \text{ at 2nd draw}) = \left(\frac{N-1}{N}\right) \times \left(\frac{1}{N-1}\right) = \frac{N-1}{N(N-1)} = \frac{1}{N}
\]
Step 4: Final Answer
The probability of selecting a specific unit at the second draw in SRSWOR is \( \frac{1}{N} \).