Probability Topics: Probability Lab (edited: Teegarden)
Summary: This module presents students with a lab exercise allowing them to apply their understanding of Probability. In an experiment using M&Ms candies, students will calculate and compare the theoretical and empirical probabilities of drawing particular color candies at random, with and without replacement. Labs changed to incorporate mini-tabs.
Class time:
Name:
Student Learning Outcomes:
- The student will calculate theoretical and empirical probabilities.
- The student will appraise the differences between the two types of probabilities.
- The student will demonstrate an understanding of long-term probabilities.
Sum of Two Dice
Begin by looking at Theoretical probabilities for the sum of two dice. Let the value in the first row be the result for Die 1 and the value in the first column be the value for Die 2. Input the sum of the corresponding row and column in each box.
| + | 1 | 2 | 3 | 4 | 5 | 6 |
| 1 | ||||||
| 2 | ||||||
| 3 | ||||||
| 4 | ||||||
| 5 | ||||||
| 6 |
| Sum | Count | Probability |
| 2 | ||
| 3 | ||
| 4 | ||
| 5 | ||
| 6 | ||
| 7 | ||
| 8 | ||
| 9 | ||
| 10 | ||
| 11 | ||
| 12 |
Theoretical Probabilities
- P(sum less than 5) = _________________
- P(sum at least 9) = _________________
- P(sum at most 6) = _________________
- P(sum more than 7) = _________________
- P(sum between 3 and 8) = _________________
- P(sum less than 11) = _________________
Do the Experiment:
Rolling the dice
Using Minitab, simulate rolling two dice 500 times and finding the sum. Use Calc -> Random Data -> Integer, 360 rows and save in die 1, die 2. Then use the Calc -> Row Statistics. Select Sum, the two die columns and save in Sum Then use Stat -> Tables -> Tally to summarize the data. Be sure to select all four options.
| Sum | Quantity | Probability |
|---|---|---|
| 2 | ||
| 3 | ||
| 4 | ||
| 5 | ||
| 6 | ||
| 7 | ||
| 8 | ||
| 9 | ||
| 10 | ||
| 11 | ||
| 12 |
Emperical Probabilities
- P(sum less than 5) = _________________
- P(sum at least 9) = _________________
- P(sum at most 6) = _________________
- P(sum more than 7) = _________________
- P(sum between 3 and 8) = _________________
- P(sum less than 11) = _________________
Essay Questions
- How do the empirical probabilities compare to the theoretical probabiliies?
- If you increased the number of times you rolled the dice to 720, would the empirical probability values change? Rerun the simulation and record your results.
- Did the increase in trials (see (2) above) cause the empirical probabilities and theoretical probabilities to be closer together or farther apart? Why?
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This work is licensed by Mary Teegarden under a Creative Commons Attribution License (CC-BY 2.0).
Last edited by Mary Teegarden on Aug 12, 2008 2:21 pm GMT-5.