1. S U C C E S S I O N

5. Z

6. Z Scissors Paper Stone  Scissors beats paper (cuts it)  Paper beats rock (wraps it)  Rock beats scissors (blunts it)  Showing the same is a draw Rock Paper Scissors

7. Z Scissors Paper Stone Rock Paper Scissors  Create the following table to complete as you play  Play the game 30 times  Add up your tally for the Total  Fill in the 3 probabilities (these are the Total / 30) ResultTallyTotalProbability A Wins B Wins Draw

8. Which are the combined events in this game? (the events happening together) Which are the possible outcomes ? We use possibility space diagrams to show the possible outcomes of combined events – try it out! Rock Paper Scissors

9. Possibility Space Diagrams Showing all possible outcomes of events happening together

10. Scissors Paper Stone Player A Scissors PaperStone Player B Scissors DWBWB WAWA Paper WAWA DWBWB Stone WBWB WAWA D Now use it to calculate the theoretical probabilities  P(A wins) = ?  P(B wins) = ?  P(Draw) = ? Z Rock Paper Scissors

11. Possibility Space Diagrams In a possibility space diagram we list all the possible outcomes of two events happening together and we use them to find the probability of the combined events! EVENT A Possible outcomes of Event A EVENTBEVENTB Possible outcomes of Event B The COMBINED Possible Outcomes

12. Possibility Space Example Imagine throwing two coins at the same time: A blue one and a red one What are the combined possible outcomes? What is the probability of getting one heads & one tails? HT H{H, H}{H, T} T{T, H}{T, T} Blue Coin Red Coin

13. {1,1} {1,2}{1,3}{1,4}{1,5}{1,4} {2,1}{2,2}{2,3}{2,4}{2,5}{2,6} {3,1}{3,2}{3,3}{3,4}{3,5}{3,6} {4,1}{4,2}{4,3}{4,4}{4,5}{4,6} {5,1}{5,2}{5,3}{5,4}{5,5}{5,6} {6,1}{6,2}{6,3}{6,4}{6,5}{6,6}

14. Finding probabilities