User: Ariana Bouillon
In Course: M/J Mathematics 2 V9 ( 2820)
Instructor: Mrs. Susan Lafferty
08.03 Experimental Probability
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Question 1 (Essay Worth 4 points)
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.
This question is to test your knowledge rather than ours.
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To design and conduct a simulation to estimate the probability, you will need to follow these steps:
a) Design of the simulation:
1. Choose a probability tool: In this case, we can use a coin as our probability tool.
2. Assign a side of the coin to represent even house numbers (Heads) and the other side to represent odd house numbers (Tails).
3. Define a single trial: In a single trial, you will flip three coins, each representing a toss to a house. If all three coins land on Tails (odd house numbers), it means that Shelly missed all three tosses at odd-numbered houses.
b) Conduct the simulation with twenty trials and record the results:
1. Perform the simulation by flipping three coins 20 times, making sure to record the results of each trial.
2. For each trial, record whether the tosses resulted in all three Tails (odd house numbers) or not.
c) Calculate the experimental probability:
1. Determine the total number of trials where Shelly's three missed papers were all at odd-numbered houses.
2. Divide the number of successful trials (all three Tails) by the total number of trials to calculate the experimental probability.
For example, let's say you conduct the simulation with twenty trials and record the results as follows:
Trial 1: H T T (not all three Tails)
Trial 2: T T T (all three Tails)
Trial 3: H H T (not all three Tails)
...
Trial 20: T T T (all three Tails)
In this case, you had 4 successful trials (all three Tails) out of 20 total trials.
To calculate the experimental probability, divide the number of successful trials (4) by the total number of trials (20):
Experimental probability = Number of successful trials / Total number of trials = 4/20 = 0.2 = 20%