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At a game show, there are three doors marked 1, 2, and 3. A contestant can select one of three keys labeled A, B, and C and then use it to open one of the doors. The sample space showing the ways in which a contestant can select a key and a door is represented in the table below.

| | | Door 1 | Door 2 | Door 3 |
|-----|------|--------|--------|--------|
| Key | A | A-1 | | A-3 |
| | B | B-1 | B-2 | B-3 |
| | C | C-1 | C-2 | C-3 |

What is the missing term in the table? If there were two doors instead of three, what would the sample size be?

A. The missing term is A-2. The sample size would be 6.
B. The missing term is C-2. The sample size would be 8.
C. The missing term is C-2. The sample size would be 9.
D. The missing term is B-2. The sample size would be 12.

Sagot :

GinnyAnsweridn
To determine the missing term in the table and the sample size if there were two doors instead of three, let's analyze the problem step-by-step.

1. Identify the Missing Term:
- We are given a table where each key can open one of the three doors. The combinations are listed as follows:
```
Key A: A-1, _, A-3
Key B: B-1, B-2, B-3
Key C: C-1, C-2, C-3
```
- From this table, it is evident that each key is associated with all three possible door combinations. The missing term, corresponding to Key A opening Door 2, should therefore be “A-2”.

2. Determine the Sample Size if There Were Two Doors:
- If there were only two doors (instead of three), each of the three keys would still need to open 2 doors.
- The combinations would then be:
- Key A: A-1, A-2
- Key B: B-1, B-2
- Key C: C-1, C-2
- This results in each key having 2 combinations, and since there are 3 keys, the total number of combinations (sample size) is [tex]\(3 \times 2 = 6\)[/tex].

Based on this detailed analysis, the correct answer is:
A. The missing term is A-2. The sample size would be 6.
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