Experimental and Theoretical Probability In this activity, you will investigate the difference between theoretical and
experimental probability by tossing a coin.
Materials Needed
One coin
Internet access
Calculator
Coin Toss
1. When tossing a coin one time, there are only _____ possible outcomes.
What are they?
_____________________________________________________
a. P(heads) =________
b. P(tails) =_________
Theoretical
Probability
If you toss a coin 10 times, how many
heads should you get?
Percent=
10
How many tails should you get?
Percent=
10
Toss your coin 10 times. Record the
Experimental number of heads.
Probability
Toss your coin 10 times. Record the
number of tails.
Percent=
10
Percent=
10
2. Did you get the number of heads and the number of tails that you
expected when you tossed the coins?_____________________
Theoretical
Probability
If you toss a coin 20 times, how many
heads should you get?
Percent=
20
How many tails should you get?
Percent=
20
Toss your coin 20 times. Record the
Experimental number of heads.
Probability
Toss your coin 20 times. Record the
number of tails.
Percent=
20
Percent=
20
3. Did you get the number of heads and the number of tails that you
expected when you tossed the coins?_____________________
Now you will “pretend” to toss a coin 100 times! Go to the website
http://syzygy.virtualave.net/webwork/javascript/cointoss.htm and enter 100
coin tosses in the box and click on the button that says flip them. Scroll
down to the bottom to see how many heads and how many tails you have.
If you toss a coin 100 times, how
Percent=
Theoretical
many heads should you get?
100
Probability
How many tails should you get?
Percent=
100
Toss your coin 100 times. Record
Experimental the number of heads.
Probability
Toss your coin 100 times. Record
the number of tails.
Percent=
100
Percent=
100
4. Did you get the number of heads and the number of tails that you
expected when you tossed the coins?_____________________
5. What percent of heads did you get when you flipped the coin?_________
Is this number getting closer to 50% as you flip more times?_____________
Now use the website to “pretend” to toss a coin 1000 times!
If you toss a coin 1000 times, how
Theoretical
many heads should you get?
1000
Probability
How many tails should you get?
Percent=
Percent=
1000
Toss your coin 1000 times. Record
Experimental the number of heads.
Probability
Toss your coin 1000 times. Record
the number of tails.
Percent=
1000
Percent=
1000
6. Did you get the number of heads and the number of tails that you
expected when you tossed the coins?_____________________
7. What percent of heads did you get when you flipped the coin?_________
Is this number getting closer to 50% as you flip more times?_____________
FOLLOW-UP QUESTIONS
1. Based on your experience with probabilities, write a good definition
for theoretical and experimental probability.
a. Theoretical Probability-___________________________________________________
___________________________________________________
b. Experimental Probability-___________________________________________________
___________________________________________________
2. What is the difference between theoretical and experimental
probability?
________________________________________________________
________________________________________________________
3. As you added more data, did the experimental probabilities get closer
to or further away from your theoretical probabilities?
________________________________________________________
4. At the beginning of the lesson you determined that, when tossing a
coin, the probability of getting heads is
1
or 50%. Does that mean
2
that when you flip a coin twice, you will always get one head and one
tail? Why or why not?
________________________________________________________
________________________________________________________
________________________________________________________
5. When tossing a coin, the two outcomes (heads or tails) are equally
likely. That means you have the same chance of getting a head as a
tail. For each of the scenarios below, determine whether or not the
outcomes are equally likely:
Scenario
Outcomes
Equally Likely?
(yes or no)
You check the weather in Rain, Snow, Sunshine
Arizona in July.
There is a new student in The student is a boy, the
your class.
student is a girl
You guess on a multiple You get the answer right,
choice question.
you get the answer wrong.
Your teacher randomly
The day is your birthday, the
picks a day of the year to day is not your birthday.
have a class party.
6. Is tossing one coin 100 times the same as tossing 100 coins one time?
Why or why not?
___________________________________________________________
___________________________________________________________
___________________________________________________________