#1 Coin Toss
In this activity, you will investigate the difference between theoretical and experimental
probability by tossing a coin.
1. When tossing a coin one time, there are only _____ possible outcomes.
What are they?
a. P(heads) =________
b. P(tails) =_________
c.
If you toss a coin 5 times, how many heads
should you get?
Theoretical
5
Probability
If you toss a coin 5 times, how many tails
should you get?
Experimental
Probability
Toss your coin 5 times. Record the number
of heads.
Toss your coin 5 times. Record the number
of tails.
Percent=
Percent=
5
Percent=
5
Percent=
5
Did you get the number of heads and the number of tails that you expected when you
tossed the coins?_____________________
d.
Theoretical
Probability
Experimental
Probability
If you toss a coin 10 times, how many heads
should you get?
If you toss a coin 5 times, how many tails
should you get?
Toss your coin 10 times. Record the
number of heads.
Toss your coin 10 times. Record the
number of tails.
Percent=
10
Percent=
10
Percent=
10
Percent=
10
Did you get the number of heads and the number of tails that you expected when you
tossed the coins?_____________________
e.
Theoretical
Probability
Experimental
Probability
If you toss a coin 25 times, how many heads
should you get?
If you toss a coin 25 times, how many tails
should you get?
Toss your coin 25 times. Record the
number of heads.
Toss your coin 25 times. Record the
number of tails.
Percent=
25
Percent=
25
Percent=
25
Percent=
25
Did you get the number of heads and the number of tails that you expected when you
tossed the coins?_____________________
2.
What is percent of heads did you got when you flipped the coin 25 times?
________________________________________________________________________
Is this number getting closer to 50% as you flip the coin more times?
________________________________________________________________________
3.
At the beginning of the lesson you determined that, when tossing a coin, the
1
probability of getting heads is
or 50%. Does that mean that when you flip a
2
coin twice, you will always get one head and one tail? Why or why not?
________________________________________________________________________
________________________________________________________________________
________________________________________________________________________
________________________________________________________________________
4.
a. Write a definition of theoretical probability and of experimental probability.
________________________________________________________________________
________________________________________________________________________
________________________________________________________________________
b. What is the difference between theoretical probability and experimental probability?
________________________________________________________________________
________________________________________________________________________
________________________________________________________________________
BONUS
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 student
your class.
is a girl
You guess on a multiple
You get the answer right, you get
choice question.
the answer wrong.
Your teacher randomly picks The day is your birthday, the day
a day of the year to have a
is not your birthday.
class party.
#2 Chip Cup
In this activity, you will investigate the difference between independent and dependent
events by pulling chips from a cup.
1. Take your cup and count the number of chips that you have?
yellow ________
blue _________
red __________
a. If you take one chip from the cup what is the probability, written as a fraction, that you
will choose a…
yellow ________
blue _________
red __________
b. Choose one chip from the cup. Then replace it and choose another chip from the cup,
counting how many chips there are in the cup. Each time you choose a chip were there
the same number of chips in the cup?
________________________________________________________________________
________________________________________________________________________
2. The formula for the probability of independent events was P(A)·P(B).
What is the probability written as a fraction, of drawing a…
red, then yellow _________________
red, then blue ____________________
red, then red ____________________
yellow, then yellow _______________
3. Choose one chip from the cup. Do not replace it and choose another chip from the
cup. Each time you choose a chip were there the same number of chips in the cup?
________________________________________________________________________
a. Start with all the chips in your cup. Draw out a red chip and don’t replace it. What is
the probability, written as a fraction, of drawing the red chip? ___________________
b. Take your cup and count the number of chips that you have remaining in the cup.
yellow ________
blue _________
red __________
c. What is the probability of drawing each of the following each of the following colors
with a second draw, if the first chip is not replaced?
yellow ________
blue _________
red __________
4. The formula for the probability of dependent events was P(A)·P(B after A).
What is the probability written as a fraction, of drawing a…
red, then yellow _________________
red, then blue ____________________
red, then red ____________________
yellow, then yellow _______________
5.
a. Write a definition of independent events and of dependent events.
________________________________________________________________________
________________________________________________________________________
________________________________________________________________________
b. What is the difference between independent and dependent events?
________________________________________________________________________
________________________________________________________________________
________________________________________________________________________
BONUS
#3 Card Shuffle
In this activity, you will investigate the difference between permutations and
combinations by pulling chips from a cup.
1. List the permutations and combinations of selecting two cards from a set of five cards.
Find the number of permutations and combinations.
Permutations List
Combinations List
Number of permutations = _________
Number of combinations = ________
2. List the permutations and combinations of selecting three cards from a set of five
cards.
Find the number of permutations and combinations.
Permutations List
Combinations List
Number of permutations = _________
Number of combinations = ________
3.
a. What was the formula for permutation notation? ___________________________
b. Use the formula to determine if a roller coaster has room for 10 people. The people
sit single file, one after the other. How many different arrangements are possible for 10
passengers on the roller coaster?
4.
a. What was the formula for combination notation?_____________________________
b. Use the formula to determine in how many ways can 9 senators be selected from
among 100 United States senators to serve on a foreign policy committee?
5.
a. Write a definition of permutations and combinations.
________________________________________________________________________
________________________________________________________________________
________________________________________________________________________
b. What is the difference between permutations and combinations?
________________________________________________________________________
________________________________________________________________________
________________________________________________________________________
BONUS
Your partner and you may work on one computer together, playing Permutations and
Combinations Jeopardy. If they aren’t already up on the computer the website is
http://www.superteachertools.com/jeopardy/usergames/Sep201139/game1317086076.php