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Probability (Grade 12)
Daljit Dhaliwal
Sticks and Stones game
Object of the game
Be the first player to move your piece around the board past your starting point.
Set-Up: Each student should place a marker on opposite sides of the circle. The area inside the circle is used for throwing the sticks when playing the game.
Rules
Determine which player will go first.
• Player 1 throws the three sticks into the center of the circle and moves his/her piece according to the results
• Player 2 then throws the sticks and moves accordingly.
• Play continues with players alternating turns.
http://illuminations.nctm.org/Lessons/Sticks/Sticks-Demo.html
Moves and Rules
Special Rule: If one player’s marker lands on or passes another player’s, the player passed over must move his/her piece back to the starting point.
Discussion
• Which is more likely—a throw with one stick decorated or a throw with two sticks decorated?
• Which is more likely—a throw with three sticks decorated or a throw with no sticks decorated?
• Which is more likely—a throw with three sticks decorated or a throw with two sticks decorated?
• Which is more likely—a throw with no sticks decorated or a throw with one stick decorated?
Tree diagram
Probability
A measure of the likelihood of an event is called the probability of an event
• Experimental Probability: Observed probability of an event A.P(A) = number of times A occurs
total number of trials• Theoretical Probability
DDD DDB DBD BDD
BBD BDB DBB BBB
Important Vocabulary
• Trial: A trial is one repetition of an experiment
• Random Variable: A variable whose value corresponds to the outcome of a random event
• Event: A set of possible outcomes of an experiment
• Simulation: An experiment that models an actual event
Key Terms
• Simple Event: An event that consists of exactly one outcome.
• Sample Space: The collection of all possible outcomes of the experiment.
• Event Space: The collection of all outcomes of an experiment that correspond to a particular event
Conditions for a “fair game”
• a game is fair if…
– all players have an equal chance of winning, or
– each player can expect to win or lose the same number of times in the long run
www.tee-cd.com/music/html