To determine which simulation method could be used to answer questions about customers purchasing popcorn, let's break down each method and see which one matches the scenario where the probability of purchasing popcorn is 2 out of 5 customers (or 0.4):
1. Using Flipping a Coin to Record Heads:
- This method would not be suitable because flipping a typical coin only provides two outcomes: heads or tails, each with a probability of 0.5. This does not match the probability of 0.4 required in this scenario.
2. Using Spinning a Spinner to Land on Green:
- This could be an option if the spinner is designed correctly. For a spinner to match our scenario, green would need to occupy 40% of the spinner's area, reflecting the 0.4 probability of purchasing popcorn. However, ensuring an evenly divided spinner might be complex and is not directly stated here.
3. Using Rolling a Die to Get an Even Number:
- Rolling a standard die can result in one of six numbers (1, 2, 3, 4, 5, 6). Since there are three even numbers (2, 4, 6) out of six possible outcomes, the probability of rolling an even number is 3/6 = 0.5. This does not match the probability of 0.4.
4. Using Picking a Marbles (and Replacing) to Get a Red Marble:
- This method involves picking a marble from a set, and if the set is designed such that 40% of the marbles are red, then this method would match the given probability. For example, if out of 10 marbles, 4 are red and 6 are not, then the probability matches the required 0.4.
We need to record the number of times a customer purchases popcorn in 100 trials, where each trial consists of reviewing 5 customers.
Considering the methods available, the fourth option using marbles appears to be the most appropriate match:
Using Picking Marbles and Replacing the Marble:
- This means you have multiple trials where you record the outcome of drawing marbles.
- Ensure your set of marbles has been designed such that 4 out of 10 marbles are red. This will give a probability of 0.4 for drawing a red marble, corresponding to a customer purchasing popcorn.
To simulate it, you can:
- Perform 100 trials.
- In each trial, observe 5 customers.
- Count the number of purchasers in each trial.
An example result from such trials might look like:
```
[2, 2, 2, 2, 2, 3, 2, 2, 2, 3, 2, 1, 2, 2, 1, 2, 2, 2, 2, 0, 3, 2, 2, 2, 5, 0, 3, 3, 2, 4, 2, 2, 3, 4, 1, 1, 0, 1, 1, 3, 2, 1, 4, 0, 3, 2, 2, 2, 4, 1, 4, 1, 3, 1, 3, 3, 4, 4, 3, 4, 3, 2, 0, 1, 4, 1, 1, 2, 1, 2, 3, 3, 2, 2, 1, 2, 0, 3, 2, 0, 0, 3, 2, 0, 2, 3, 3, 3, 2, 2, 2, 4, 1, 2, 2, 1, 2, 3, 2, 2]
```
This result shows the number of customers who purchased popcorn out of 5 in each of the 100 trials.
