To solve this question, let's break down the problem and analyze each part step-by-step.
1. Understanding the Table:
- We have three keys: A, B, and C.
- We have three doors: 1, 2, and 3.
- The table lists combinations of keys and doors in the form "X-Y", where X is the key and Y is the door number.
2. Initial Table Analysis:
- The table is partially filled. We are given:
- A -> A-1, (missing), A-3
- B -> B-1, B-2, B-3
- C -> C-1, C-2, C-3
- From this, we can see that each key should match with each door once. Therefore, the missing term in the table where Key A intersects with Door 2 should be "A-2".
3. Calculating the Initial Sample Size:
- In the initial scenario, we have 3 keys and 3 doors.
- The sample size can be calculated by multiplying the number of keys by the number of doors:
[tex]\[
\text{Initial Sample Size} = 3 \times 3 = 9
\][/tex]
4. Calculating the Reduced Sample Size:
- If we reduce the number of doors to 2 while keeping the number of keys the same (3 keys: A, B, C; 2 doors: 1, 2), the new sample size can be calculated as:
[tex]\[
\text{Reduced Sample Size} = 3 \times 2 = 6
\][/tex]
5. Conclusion:
- The missing term in the table is "A-2".
- If there were only two doors, the sample size would be 6.
So, the correct answer is:
A. The missing term is A-2. The sample size would be 6.
