Shelly delivers the weekly local paper to neighborhoods in her town. House numbers are even on one side of the street and odd on the other. Shelly delivers an equal number of papers to both sides of the street. Although she always aims for the front doorstep, Shelly typically misses on three of the tosses on her route each week. Design and conduct a simulation to estimate the probability that next week, Shelly's three misses will all be at odd-numbered houses.

Hint: You can set up the experiment using 3 coins to collect the data. Allow one side of the coin to represent Heads (evens) and one other side to represent Tails (odds).

a) Explain clearly your design of the simulation, including choice of probability tool and description of a single trial.
b) Conduct the simulation with twenty trials and record the results.
c) Calculate the experimental probability that all 3 of Shelly's missed papers will be at odd-numbered houses.

a)

To design the simulation, we will use a probability tool such as a coin. We'll assign one side of the coin to represent Heads (evens) and the other side to represent Tails (odds).

For each trial, we will simulate each toss by flipping the coin three times. If the result is Tails (odds) for all three tosses, we will count it as a "success" because it represents Shelly missing all three tosses at odd-numbered houses. If the result is any other combination (e.g., Heads-Heads-Heads or Heads-Tails-Heads), we will count it as a "failure" because it represents Shelly missing at least one toss at an even-numbered house or a combination of even and odd-numbered houses.

We will repeat this process for a defined number of trials (in this case, 20) to collect data and estimate the probability of all three misses happening at odd-numbered houses.

b)

To conduct the simulation, we will flip the coin three times for each trial and record the results. Here are the outcomes for 20 trials:

1. Tails-Tails-Tails (success)
2. Heads-Tails-Tails (failure)
3. Tails-Heads-Tails (failure)
4. Heads-Tails-Tails (failure)
5. Tails-Tails-Tails (success)
6. Tails-Tails-Heads (failure)
7. Heads-Heads-Heads (failure)
8. Heads-Tails-Heads (failure)
9. Tails-Tails-Tails (success)
10. Heads-Heads-Tails (failure)
11. Tails-Heads-Tails (failure)
12. Tails-Heads-Heads (failure)
13. Tails-Tails-Tails (success)
14. Heads-Heads-Tails (failure)
15. Heads-Tails-Heads (failure)
16. Heads-Heads-Heads (failure)
17. Tails-Heads-Heads (failure)
18. Heads-Tails-Tails (failure)
19. Heads-Heads-Heads (failure)
20. Tails-Heads-Heads (failure)

c)

To calculate the experimental probability that all three of Shelly's missed papers will be at odd-numbered houses, we need to find the ratio of successful trials (where all three tosses were Tails) to the total number of trials (20 in this case).

From the outcomes recorded above, we can see that there were 4 successful trials (Tails-Tails-Tails) out of 20 trials total.

Experimental probability = Number of successful trials / Total number of trials
Experimental probability = 4/20
Experimental probability = 0.2

Therefore, the experimental probability that all three of Shelly's missed papers will be at odd-numbered houses is 0.2, or 20%.