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Activity 1: Experimental and Theoretical Probability
1. Rolling a single standard die
The sample space of an experiment is the set of all possible outcomes.
1. What is the sample space for each roll of a die? {________________________}
2. If the die is perfectly balanced, will all the possible outcomes be equally
likely? _______________________________
3. Complete the following table by rolling your die 50 times and keeping track of
the outcomes, that is, how many ones did you get? How many two’s? Do the
same for each possible outcome. Then calculate the experimental probability
of every outcome as the ratio:
(# of times you get the outcome)/ (total # of rolls)
and write your results in the table.
Outcome
Experimental Experimental
# of
Probability probability
times
as a fraction as a decimal
1
2
3
4
5
6
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4. Write the second column of your table in the space at front designated by
your teacher.
5. What should be the sum of the entries in the second column?__________
The theoretical probability of an event is defined as the ratio: (# of favorable
cases)/(total # of possible cases. Thus to get the theoretical probability of
obtaining a five when rolling a die once you proceed as follow:
6. How many possible fives can you get when you roll a die once? _____
7. How many possible outcomes can we have by rolling a die? _______
8. So, what is the theoretical probability of getting a five when you roll a die
#of favorable outcomes
once?

# of possible outcomes
9. What is the theoretical probability of getting a three when you roll a die once?
#of favorable outcomes

# of possible outcomes
Complete the following table
# of
# of
Theoretical Theoretical
Outcome favorable possible Probability probability
outcomes outcomes as a fraction as a decimal
1
2
3
4
5
6
10. Since all the outcomes are equally likely, what is the theoretical probability of
getting any outcome of the sample space when you roll a die once? ________
11. Are your results for experimental and theoretical probability the same?
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12. Collect the second column of the first table of everyone in the class, add all
the outcomes for one and write it in the table below. Repeat the process for
every possible outcome. Then fill in the rest of the table
Experimental Experimental
# of
Outcome
Probability probability
times
as a fraction as a decimal
1
2
3
4
5
6
13. How do the results of this table compare with the theoretical probabilities you
obtained in your second table? What do you notice?
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A Quesada Director Project AMP