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.

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 DDDDDBDBDBDD BBDBDBDBBBBB

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