At a game show, there are three doors marked 1, 2, and 3. A contestant is allowed to 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.

Door
1 2 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 doors, 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.

Answer:

It is A

Step-by-step explanation:

The answer is A. The missing term is A-2. The sample size would be 6.

a. To answer the question, we need to know what sample space is.

A sample space is the total number of possible outcomes of an event.

Now, since there are Doors 1, 2 and 3 and Keys A, B and C. The sample space is

Key A: A-1, A-2, A-3

Key B: B-1, B-2, B-3

Key C: C-1, C-2, C-3

So, the missing item is A-2.

b.

The sample size would be 6.

To answer the question, we need to know what sample size is.

The sample size is the size of the sample space.

If there were two doors instead of 3, the sample size would be since we have 2 doors and 3 keys. The sample size is 2 × 3 = 6.

So, the sample size would be 6.

So, the answer is A. The missing term is A-2. The sample size would be 6.

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