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Probability Topics: Probability Lab (edited: Teegarden)

Module by: Mary Teegarden. E-mail the author

Based on: Probability Topics: Probability Lab by Barbara Illowsky, Ph.D., Susan Dean

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.

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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.

Table 1
+ 1 2 3 4 5 6
1            
2            
3            
4            
5            
6            
Table 2: Theoretical Probabilities
Sum Count Probability
2    
3    
4    
5    
6    
7    
8    
9    
10    
11    
12    

Theoretical Probabilities

  1. P(sum less than 5) = _________________
  2. P(sum at least 9) = _________________
  3. P(sum at most 6) = _________________
  4. P(sum more than 7) = _________________
  5. P(sum between 3 and 8) = _________________
  6. 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.

Table 3: Emperical Probabilities
Sum Quantity Probability
2    
3    
4    
5    
6    
7    
8    
9    
10    
11    
12    

Emperical Probabilities

  1. P(sum less than 5) = _________________
  2. P(sum at least 9) = _________________
  3. P(sum at most 6) = _________________
  4. P(sum more than 7) = _________________
  5. P(sum between 3 and 8) = _________________
  6. P(sum less than 11) = _________________

Essay Questions

  1. How do the empirical probabilities compare to the theoretical probabiliies?
  2. 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.
  3. 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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