Download Experiments in Theoretical Probability

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Activity 1: Experimental and Theoretical Probability
Experiment #1. Rolling a single standard die
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.
Experimental Experimental
# of
Outcome
Probability probability
times
as a fraction as a decimal
1
2
3
4
5
6
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Antonio R. Quesada Director Project AMP
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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
#of favorable outcomes
once? P(5)=

# of possible outcomes
9. What is the theoretical probability of getting a three when you roll a die once?
#of favorable outcomes
P(3)=

# 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
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Antonio R. Quesada Director Project AMP
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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.
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 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?
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S 05
Antonio R. Quesada Director Project AMP
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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?
# of
Outcome
times
Experimental
Probability as a
fraction
Experimental
probability as a
decimal
H
T
4. What is the theoretical probability of getting heads when you toss a coin
#of favorable outcomes
once? P(H)=

# of possible outcomes
5. Now complete the following table with the theoretical probabilities
# of
# of
Theoretical Theoretical
Outcome favorable possible Probability probability
outcomes outcomes as a fraction 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
Experimental Experimental
# of
Probability probability
times
as a fraction as a decimal
H
T
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Antonio R. Quesada Director Project AMP
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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?
Project Amp
S 05
Antonio R. Quesada Director Project AMP