Probability and Statistics
Focus: Applications of Statistics and Probability
The student will investigate and describe the difference between the experimental probability and theoretical probability of an event. 


Essential Knowledge and Skills 
 Determine the theoretical probability of an event.
 Determine the experimental probability of an event.
 Describe changes in the experimental probability as the number of trials increases.
 Investigate and describe the difference between the probability of an event found through experiment or simulation versus the theoretical probability of that same event.

Essential Understandings 
 What is the difference between the theoretical and experimental probability of an event? Theoretical probability of an event is the expected probability and can be found with a formula. The experimental probability of an event is determined by carrying out a simulation or an experiment. In experimental probability, as the number of trials increases, the experimental probability gets closer to the theoretical probability.


Vertical Articulation 
 SOL 5.14  make predictions/determine
probability by constructing a sample
space
 SOL 6.16ab  a) compare/contrast dep/indep
events; b) determine probabilities
for dep/indep events
 SOL 8.12  determine probability of
indep/dep events with and without
replacement

Instructional Materials 
 VDOE Enhanced Scope and Sequence Lesson: What Are the Chances? (PDF)  Investigating and describing the theoretical and experimental probabilities (Word)
 Notes: Probability Basics (ppt)
 Activity: Probability Stations (doc)
 Activity: Mathematician Game (pdf)
 Activity: What is the Probability (pdf)
 Guided Notes: Theoretical and Experimental Probability (doc)
 VDOE Algebra Readiness Curriculum Companion: Exploring Probability (pdf)

Real World Lessons 

Practice 
 Worksheet: Calculating Probability (pdf)
 Worksheet: Probability (pdf)

SOL Mini Quiz 
 SOL 7.9 Mini Quiz: Probability (pdf)  (doc)

Skills 
 Mathematics Assessment Project:
 A10:Card Game  Apprentice  In this task, you will use probability to make predictions about a card game.
 E06:Lottery  Expert  In this task, you must use math to decide whether a lottery idea will make money.
 Experimental Probability: Amusement Park Fun (doc)
 Probability: Random Dots (doc)

Videos 
 YouTube:
Probability  Theoretical Probability versus Experimental Probability
 PH: Finding experimental probability
 PH: Finding theoretical probability
 PH: Using probability to make predictions about populations
 PH: Finding experimental probability using simulations

Explore
Learning 
 Probability Simulations: Experiment with spinners and compare the experimental probability of particular outcomes to the theoretical probability. Select the number of spinners, the number of sections on a spinner, and a favorable outcome of a spin. Then tally the number of favorable outcomes.
 Spin the Big Wheel! (Probability): Step right up! Spin the big wheel! Each spin can result in no prize, a small prize, or a big prize. The wheel can be spun by 1, 10, or 100 players. Results are recorded on a frequency table or a circle graph. You can also design your own wheel and a sign that describes the probabilities for your wheel.
 Theoretical and Experimental Probability: Experiment with spinners and compare the experimental probability of a particular outcome to the theoretical probability. Select the number of spinners, the number of sections on a spinner, and a favorable outcome of a spin. Then tally the number of favorable outcomes.

Websites 
 Illuminations  What Are My Chances?
 Interactive Lab  Glencoe practice problems.
 Probability Games  Have a little fun while exploring the concepts of probability.
 Johnnie's Math Page  Probability
 LearnAlberta  Probability

VDOE Interventions 
 VDOE Algebra Readiness Curriculum Companion: Exploring Probability  The lessons focus on creating sample spaces and using the Fundamental (Basic) Counting
Principle. Students calculate experimental probability through games and then calculate the theoretical
probability. (pdf)

Common Core
Standards 
