Theoretical and Experimental Probability
Take a moment to discuss the title of today’s lesson with your group. What do you think the difference is
between THEORETICAL and EXPERIMENTAL probability?
Theoretical Probability
Experimental Probability
_____________________ _____________________ is the ratio of favorable outcomes to possible outcomes.
_____________________ _____________________is the ratio of the number of times an event actually occurred to the
number of trials completed.
Example 1:
When rolling a fair number cube (numbered 1-6), what is the theoretical probability of rolling a 2?
The table below shows the results of rolling a number cube 50 times.
What was the experimental probability of rolling a 2?
What was the theoretical probability of rolling a 6?
Example 2: The bar graph shows the results of spinning the spinner below 200 times. Complete the table to show the
theoretical and experimental probabilities of landing on each number.
Experimental
Probability
1
2
3
4
5
Theoretical
Probability
Using Probability to Make Predictions
1. It rained 2 out of the last 12 days of March. If this trend continues, how many rainy days would you expect to have in
April? (there are 30 days in April).
Hint: think of how we solve using unit rates, scale drawings, like units on a diagonal…
2. There are 105 lettered tiles in a board game. You choose the
tiles shown. How many of the 105 tiles would you expect to be
vowels?
3. You have a package of 20 assorted thank-you cards. You pick the
four cards shown. How many of the 20 cards would
you expect to have flowers on them?
4. The theoretical probability that a pop song plays on your MP3 player is 0.45. There are 80 songs on your MP3 player.
How many of the songs are pop songs?
5. You check 20 cartons of eggs. Three of the cartons have at least one cracked egg. If a shipment contains 400 cartons
of eggs, how many cartons would you expect to contain at least one cracked egg?