Experiment #1. Rolling a single standard die
1
1.
What are all the possible outcomes of rolling a die?
{________________________}
In any experiment, the set of all possible outcomes is called the sample space of an experiment.
2.
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
# of times
Experimental Experimental
Probability as a fraction probability as a decimal
1
2
3
4
5
6
Project Amp S 05 Antonio R. Quesada Director Project AMP

2
3.
Write the second column of your table in the space at front designated by your teacher.
4.
What should be the sum of the entries in the second column?__________
5.
If the die is perfectly balanced, will all the possible outcomes be equally likely? _______________________________
If all the possible outcomes of an experiment are equally likely, 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 once? P(5)=
# of favorable outcomes
# of possible outcomes

9.
What is the theoretical probability of getting a three when you roll a die once?
P(3)=
# of favorable outcomes
# of possible outcomes

Complete the following table
Outcome
# of favorable outcomes
# of possible outcomes
Theoretical
Probability as a fraction
Theoretical probability as a decimal
1
2
5
6
3
4
Project Amp S 05 Antonio R. Quesada Director Project AMP

3
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?
12.
Collect the second column of the first table of everyone in the class, add all the second columns and write it in the table below. Then fill in the rest of the table.
Outcome
# of times
Experimental Experimental
Probability as a fraction probability as a decimal
1
2
3
4
5
6
13.
How do the results of this table compare with those of the theoretical probabilities you obtained in your second table? What do you notice?
14.
If you roll the dice thousands and thousands of times, how will the results of the experimental probabilities compare with the theoretical probabilities?
Project Amp S 05 Antonio R. Quesada Director Project AMP

Experiment #2: Tossing a balance coin
Let’s consider now the experiment of tossing a well balanced coin.
1.
What are the possible outcomes of this experiment?___________
2.
What is the sample space of this experiment?{__________________}
3.
Complete the following table by tossing your coin 20 times and keeping track of the outcomes, that is, how many heads did you get? How many tails?
Outcome
H
# of times
Experimental
Probability as a fraction
Experimental probability as a decimal
T
4.
What is the theoretical probability of getting heads when you toss a coin once? P(H)=
# of favorable outcomes
# of possible outcomes

5.
Now complete the following table with the theoretical probabilities
Outcome
# of favorable outcomes
# of possible outcomes
Theoretical Theoretical
Probability as a fraction probability as a decimal
H
T
5.
Collect the second column of the first table of everyone in the class, add all the second columns and write it in the table below. Then fill in the rest of the table.
Outcome
# of times
Experimental Experimental
Probability as a fraction probability as a decimal
H
T
4
Project Amp S 05 Antonio R. Quesada Director Project AMP

6.
How do the results of this table compare with those of the theoretical probabilities you obtained in your second table? What do you notice?
7.
If you roll the dice thousands and thousands of times, how will the results of the experimental probabilities compare with the theoretical probabilities?
5
Project Amp S 05 Antonio R. Quesada Director Project AMP