Let's solve the given problems step by step.
### Problem 1: Finding the Missing Term
The table represents the sample space showing ways in which a contestant can select a key and a door. Each combination of key and door results in an entry in the table.
Given Table:
\begin{tabular}{|c|c|c|c|c|}
\hline & & \multicolumn{3}{|c|}{ Door } \\
\hline & & 1 & 2 & 3 \\
\hline \multirow{4}{}{ Key } & A & A-1 & & A-3 \\
\hline & B & B-1 & B-2 & B-3 \\
\hline & C & C-1 & C-2 & C-3 \\
\hline
\end{tabular}
Each combination should have a unique label in the format key-door. Given below are the entries:
- For Key A and Doors:
- Door 1: A-1
- Door 2: Missing
- Door 3: A-3
- For Key B and Doors:
- Door 1: B-1
- Door 2: B-2
- Door 3: B-3
- For Key C and Doors:
- Door 1: C-1
- Door 2: C-2
- Door 3: C-3
The missing term for Key A and Door 2 should follow the same format, so it is A-2.
### Problem 2: Sample Size with Two Doors
Now, consider the scenario where there are three keys (A, B, C) and only two doors (1, 2) instead of three doors.
Each key can be paired with each door. Therefore, the total number of ways (sample size) to select a key and a door is calculated by:
- Number of keys × Number of doors
Given:
- Number of keys = 3
- Number of doors = 2
So, the sample size = 3 keys 2 doors = 6.
### Conclusion
Therefore, the answers to the given questions are:
- The missing term in the table is A-2.
- If there were two doors instead of three, the sample size would be 6.
Hence, the correct option is:
A. The missing term is A-2. The sample size would be 6.
