Probability Lab
The following activities will help students understand various aspects of probability.
Station 1 – Game Cube: Theoretical versus experimental probability. Theoretical probability is
the probability of an event based solely on calculation.
A.
B.
C.
D.
E.
F.
G.
What is the theoretical probability of rolling a 1 on the game cube? ______
What is the theoretical probability of rolling a 2 on the game cube? ______
What is the theoretical probability of rolling a 3 on the game cube? ______
What is the theoretical probability of rolling a 4 on the game cube? ______
What is the theoretical probability of rolling a 5 on the game cube? ______
What is the theoretical probability of rolling a 6 on the game cube? ______
What is the probability of rolling a 1, 2, 3, 4, 5 or 6? _______
Experimental probability is the probability of an event passed on what has happened before (in
an experiment). It is determined by recording results and using data.
H. Each team member gets one cube. Roll it 20 times and record the results on the table
under “individual rolls” using tally marks for each of the 6 numbers on the cube:
#
Individual
rolls
Total team
rolls
Experimental
Probability
1
2
3
4
5
6
Overall team total:
I. For each game cube number, add the totals for each team member together and record
it under “total team rolls”
J. Calculate the experimental probability for each number by dividing the total team rolls
for each number by the overall total number of rolls. Record them on the table under
“experimental probability.”
K. How do the experimental probabilities compare to the theoretical probabilities?
Station 2 – Bag of Tiles. Independent versus dependent events
A. Record the number of each color tile in the bag
a. Red ________
b. Blue ________
c. Green _______
d. Total________
B. What is the theoretical probability of picking a red tile without looking? ______
C. What is the theoretical probability of picking a blue tile without looking? ______
D. What is the theoretical probability of picking a green tile without looking? ______
E. What is the theoretical probability of picking a red, blue OR green tile without looking?
______
Independent events are events that are not affected by the outcome of the previous event. If
you put any tile you pick back in the bag before picking again, you have independent events.
The second pick is not affected by the first.
For example, to find the probability of drawing a Red tile and then a blue tile if you replace the
red tile after picking it, you need the probabilities of both events and you multiply them
together:
F. Probability of picking a red tile first: _______
G. Does the probability of picking a blue tile change once the red tile is returned to the
bag? ______
H. Probability of picking a blue tile: _______
I. Multiply the two probabilities together:
Dependent events are events that change their probability because of the first event. Not
replacing a tile changes the number of tiles in the bag as well as the number of the color picked.
The probability for later picks has changed.
For example, to find the probability of drawing a red tile and then blue tile if you do NOT
replace the red tile, you follow the steps below:
J.
K.
L.
M.
Probability of picking a red tile first: _______
How many tiles are now in the bag total? _______
Now what is the probability of picking the blue tile? _______
Multiply the two probabilities together:
Station 3 - Cards. Dependent and Independent Events
A. How many suits are in a standard deck of cards: _______
B. What is the probability of picking a spade: _______
C. What is the probability of picking a heart: _______
D. What is the probability of picking a diamond: _______
E. What is the probability of picking a club: _______
F. What is the probability of picking a card (club, diamond, heart OR spade): ______
G. How many of each number are in the deck (2, 3, 4, etc): ______
H. How many of each suit are in the deck (how many clubs, etc): _______
I. How many cards in the deck: _____
J. What is the probability of picking a King: _____
K. What is the probability of picking the King of Diamonds: ______
Independent events are events that are not affected by the outcome of the previous event.
For example, to find the probability of drawing two Hearts if you replace the first heart after
you pick it, you need the probabilities of both events and you multiply them together:
L. Probability of picking the first heart: _______
M. Does the probability of picking a heart change once the first heart is returned to the
deck? ______
N. Probability of picking a heart the second time: _______
O. Multiply the two probabilities together:
Dependent events are events that change their probability because of the first event.
For example, to find the probability of drawing two hearts in a row if you DO NOT replace the
first heart, you follow the steps below:
P.
Q.
R.
S.
T.
Probability of picking a heart first: _______
How many cards are in the deck now? _______
How many hearts are in the deck now? ______
Now what is the probability of picking the second heart? _______
Now calculate the probability by multiplying the probabilities of the two events:
Station 4. Box Model. Theoretical versus experimental probability.
Theoretical probability is the probability of an event based solely on math. Experimental
probability is the probability based on actual experience. Using the computer Box Model
program, choose 4 numbers to put in the box by clicking on the numbers.
A. What is the theoretical probability of picking each number? _____
B. How many numbers do you expect to be drawn before each number is picked once?
_____
C. Select “start” on the program and hit pause when all the numbers have been chosen
once. How many total picks did it take? ______
D. Select “Show Theoretical probability”. Compare the theoretical probability and the
experimental probability at this point:
E. Select “Quick draw” and enter 1000. Hit start again.
F. How does the experimental probability compare to the experimental probability after
1000 more picks?
Select the back button and find the coin toss program.
A. What is the theoretical probability of getting “heads”?________
B. Select “Number of Tosses” and enter 100.
C. Select “Start” and watch the bars move up and down as the experimental probability
changes based on the results. This shows that experimental probability changes all the
time as a result of the latest experience.
D. Record the results of your experiment under the trial 1 column:
Trial
1
2
3
Number of Heads
Number of Tails
Longest Run of Heads
Longest Run of Tails
Percentage of Heads
E. Repeat the experiment 2 more times and record the results.
F. Does experimental probability change? ________
G. What is the theoretical probability of getting your longest run of heads?________