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Question

steps and randomly choose left or right as the direction each time.
Which of these tables lists all possible outcomes of your random walk? (Each row represents one outcome.)
Choose all answers that apply:
Choose all answers that apply:
(Choice A) Table A
A
Table A
(Choice B) Table B
B
Table B
Table A:
First Second Third
Left Left Left
Left Left Right
Left Right Left
Left Right Right
Right Left Left
Right Left Right
Right Right Left
Right Right Right
Table B:
First Second Third
Right Right Right
Left Right Right
Right Left Right
Left Left Right
Right Right Left
Left Right Left
Right Left Left
Left Left Left

Answer 1

To determine which table contains all possible outcomes of a random walk consisting of three steps, where each step can be either "Left" or "Right," we need to identify all combinations of these two directions across three steps.

Each step has 2 possible directions, and for 3 steps, we can calculate the total number of outcomes as \(2^3 = 8\).

The possible combinations (outcomes) for 3 steps are:

1. Left, Left, Left (LLL)
2. Left, Left, Right (LLR)
3. Left, Right, Left (LRL)
4. Left, Right, Right (LRR)
5. Right, Left, Left (RLL)
6. Right, Left, Right (RLR)
7. Right, Right, Left (RRL)
8. Right, Right, Right (RRR)

Now, let's check both tables to see if they include all these combinations:

Table A:

1. Left, Left, Left (LLL)
2. Left, Left, Right (LLR)
3. Left, Right, Left (LRL)
4. Left, Right, Right (LRR)
5. Right, Left, Left (RLL)
6. Right, Left, Right (RLR)
7. Right, Right, Left (RRL)
8. Right, Right, Right (RRR)

All outcomes are represented in Table A.

Table B:

1. Right, Right, Right (RRR)
2. Left, Right, Right (LRR)
3. Right, Left, Right (RLR)
4. Left, Left, Right (LLR)
5. Right, Right, Left (RRL)
6. Left, Right, Left (LRL)
7. Right, Left, Left (RLL)
8. Left, Left, Left (LLL)

Table B does not include the combination "Left, Left, Left" and "Left, Right, Right." Therefore, it is missing outcomes and does not cover all the combinations.

Conclusion:

• Table A is correct.
• Table B is not correct.

So, the answer to choose is:

• (Choice A) Table A