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You've decided to take


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

1 answer

To determine which table accurately lists all possible outcomes of a random walk involving a number of steps or directions, we need to understand what a random walk consists of. A random walk of \( n \) steps in a two-direction scenario (left or right) generates \( 2^n \) possible outcomes.

Assuming you are considering a 3-step random walk (based on the structure of Table A), we would list all combinations of left (L) and right (R) movements. The possible outcomes can be generated as follows:

  1. LLL
  2. LLR
  3. LRL
  4. LRR
  5. RLL
  6. RLR
  7. RRL
  8. RRR

Now let's look at the outcomes provided in Table A:

  • LLL
  • LLR
  • LRL
  • LRR
  • RLL
  • RLR
  • RRL
  • RRR

Table A includes all the combinations for a random walk of 3 steps, where each row represents a different outcome.

Now, we need to evaluate if there's another "Table B," which was not provided in your question, but you will need to compare its outcomes to ensure they present the exact same combinations as shown above.

If Table B has different outcomes or misses any of the combinations, then Table A would stand correct as the complete representation of the possible outcomes for a 3-step random walk left or right.

If you provide contents of Table B, I could assist you in comparing the two tables and determining if they both represent the same set of possible outcomes.