S U C C E S S I O N P(N chosen) = 1 10 P(S chosen) = 3 10 P(vowel chosen)= 4 10 = 2 5 P(S not chosen) = 1- 3 10 = 7 10

P(ace) = 4 52 = 1 13 P(a spade) = 13 52 = 1 4 P(not a club) = 1- 1 4 = 3 4 P( 7 or 8)= 8 52 = 2 13 P(not 7 or 8) = 1 - 2 13 = 11 13

P(red)= 15 22 P(not red) = 1− 15 22 = 7 22 P(black) = 1 22 P(red or white) = 16 22 = 8 11 P(not red or white) = 1− 8 11 = 3 11

P(made in Japan)= 24 60 = 2 5 P(not made in Britain) = 1− 22 60 = 19 30 P(made in Europe not Britain) = 14 60 = 7 30 P(made in America)= 0

Z

Rock Paper Scissors Scissors Paper Stone Z Rock Paper Scissors 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 Scissors Paper Stone A Wins B Wins Draw Z Rock Paper Scissors Scissors Paper Stone 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) Result Tally Total Probability A Wins B Wins Draw

(the events happening together) Rock Paper Scissors 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!

Possibility Space Diagrams Showing all possible outcomes of events happening together

Rock Paper Scissors D WB WA Scissors Paper Stone P(A wins) = ? Z Rock Paper Scissors Scissors Paper Stone Now use it to calculate the theoretical probabilities P(A wins) = ? P(B wins) = ? P(Draw) = ? Player A Scissors Paper Stone Player B D WB WA

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 E V E N T B Possible outcomes of Event B The COMBINED Possible Outcomes

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? Blue Coin H T {H, H} {H, T} {T, H} {T, T} Red Coin Possible Outcomes curly brackets!

{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}