Experimental Probability and Simulation Analysis
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3. Andreas is performing an experiment involving rolling a number cube. He rolls the number cube 60 times and records the results in the table.
A. MP Construct Arguments Do you think the outcomes are equally likely? Explain.
B. Find the experimental probabilities to complete the table.
| Outcome | Frequency | Experimental Probability |
| :--- | :--- | :--- |
| 1 | 8 | |
| 2 | 11 | |
| 3 | 10 | |
| 4 | 7 | |
| 5 | 11 | |
| 6 | 13 | |
4. Open Ended Ask 8 students how many letters are in their first name. Record the number of letters for each answer. Describe one event from your experiment and find the experimental probability of this event.
5. MP Use Tools A football quarterback completes $60\%$ of attempted passes. Describe a simulation that you can perform in order to predict how many passes out of 40 this quarterback will complete.
6. Jean estimates that her friend completes a new level of a video game on the first try $20\%$ of the time. She conducts a simulation to predict how many times out of 80 her friend would complete a new level on the first try. Jean uses a random number generator. Every digit that is 8 or 9 represents completing the level. What is the probability that her friend completes a new level on the first try, written as a percent?
| Digit | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
| :--- | :--- | :--- | :--- | :--- | :--- | :--- | :--- | :--- | :--- | :--- |
| Frequency | 10 | 9 | 6 | 7 | 8 | 12 | 4 | 6 | 7 | 11 |
This question includes visual content: The image contains two tables and a decorative illustration. Table 1: Three columns titled 'Outcome' (values 1-6), 'Frequency' (values 8, 11, 10, 7, 11, 13), and 'Experimental Probability' (empty). Next to it is an illustration of colorful dice (purple, yellow, blue, red). Table 2: Two rows titled 'Digit' (values 0-9) and 'Frequency' (values 10, 9, 6, 7, 8, 12, 4, 6, 7, 11).
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Let's work through problem number 6. Jean is simulating her friend's video game performance using a random number generator. We need to find the experimental probability of her friend completing a level on the first try, based on the provided data.
Problem 6: Experimental Probability Analysis
According to the problem, the digits eight and nine represent the event 'completing the level'.
First, we look at the frequency table to find the number of times these specific digits occurred. Digit eight appeared seven times, and digit nine appeared eleven times.
By adding these two frequencies together, we get a total of eighteen successful outcomes out of the simulation trials.
The problem states Jean conducted eighty trials in total. To find the experimental probability, we divide the eighteen successes by the eighty total trials.
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