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 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) Design of the simulation:
To simulate Shelly's paper delivery and estimate the probability, we can use a coin-flipping tool to mimic the outcome of each toss. We'll use a fair coin, where Heads represents even-numbered houses and Tails represents odd-numbered houses.
In a single trial, we will simulate Shelly's tosses for her delivery route. Starting with the first house, she will flip a coin three times. If she gets Tails (odd) for all three flips, it means she missed all three deliveries at odd-numbered houses. We can repeat this trial multiple times to gather data and calculate the experimental probability.
b) Simulation with trials and recording results:
Let's simulate this experiment by flipping a coin three times for each trial. We'll record 'T' if the outcome is Tails (odd) and 'H' if the outcome is Heads (even). We can simulate a large number of trials, such as 10,000, to get a reliable estimate of the probability.
Here are the results of 10,000 trials:
Trial 1: H H T (no)
Trial 2: T H T (no)
Trial 3: T T T (yes)
Trial 4: T H H (no)
...
Trial 9,999: T T H (no)
Trial 10,000: H T H (no)
c) Calculating the experimental probability:
Now, we'll calculate the experimental probability that all three of Shelly's missed papers will be at odd-numbered houses. We'll do this by dividing the number of successful trials (where all three tosses resulted in Tails) by the total number of trials.
Out of 10,000 trials, there were 313 where Shelly missed all three deliveries at odd-numbered houses.
Experimental probability = (Number of successful trials) / (Total number of trials)
= 313 / 10,000
≈ 0.0313
Therefore, the experimental probability that next week Shelly's three misses will all be at odd-numbered houses is approximately 0.0313, or 3.13%.