MDM4U
1.3 Comparing Experimental and Theoretical Probability
Learning Goals
I am learning to

Recognize the difference between experimental probability and theoretical probability
Investigate 1 Three-Coin-Flip Simulation
In this activity you will compare the experimental probability to the theoretical probability when three fair
coins are flipped.
1. Draw a tree diagram to show all possible outcomes. Examine the sample space. How many possible
outcomes are there?
2. What is the theoretical probability that there will be:
a) Exactly three heads
b) Exactly two heads
c) Exactly one head
d) No heads
Combine real trials
3. a) Using 3 coins, you and a partner will perform an experiment by performing real trials. Flip 3 coins
10 times. Record your data below.
0 Heads
1 Head
2 Heads
3 Heads
Determine the experimental probability of each outcome based on these 10 trials. Compare these
values with the theoretical probabilities calculated in #2 above. How close are they?
b) Combine trials with your classmates until you have 100 trials in total. Sketch a bar graph of the
results. How does the graph compare to the theoretical prediction?
c) Combine trials with your classmates until you have 1000 trials in total. Sketch a bar graph of the
results. How does the graph compare to the theoretical prediction?
4. Reflect Explain what happens to the statistical probabilities of this experiment as the total number
of trials increases.
Investigate 2 Dice Simulation using Fathom Software
The table below illustrates all possible outcomes for the sum of the dice when two standard dice are
thrown.
1. What is the theoretical probability of throwing each sum?
Event A, Sum
2
3
4
5
6
7
8
9
10
11
12
P(A)
2. Sketch a bar graph showing the theoretical probability of rolling each sum.
3.
Use the statistics software FathomTM (installed on computers in the library and computer lab, or
you can install it at home with the installation CD available from Mr. Meli or the school library) to
conduct this experiment for a large number of trials. Follow the instructions on the following page.
Homework
p. 32 #1, 2, 5, 6, 8, 10