Probability Topics: Probability Lab (edited: Teegarden)
1.1
2008/08/12 14:21:12.360 GMT-5
2008/08/12 14:21:48.364 GMT-5
Mary
T
Teegarden
tteegard@sdccd.edu
Mary
T
Teegarden
tteegard@sdccd.edu
elementary
exercise
homework
lab
long-term
probability
replacement
statistics
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 DiceBegin 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
Theoretical Probabilities
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 diceUsing 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.
Emperical Probabilities
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?