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# Tree diagrams

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lesson to introduce the use of tree diagrams to determine probability.
Adapted from cbillet @ Kidderminster College.

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### Tree diagrams

1. 1. Tree DiagramsLearning Intention:Draw and use a tree diagram to find conditional probabilities.
2. 2. Z
3. 3. Z Scissors Paper Stone  Create the following table to complete as you play Result Tally Total Probability A Wins B Wins Draw  Play the game 30 times  Add up your tally for the Total Scissors beats paper (cuts it)  Fill in the 3 probabilities (these are the Total / 30) Paper beats stone (wraps it)  Use the calculator these into Stone beats scissors (blunts it) convert these into decimals  Enter your results into the Showing the same is a draw class spreadsheet
4. 4. Z Scissors Paper StoneCan you find a way to calculate the probabilities of the game usinga tree diagram? Scissors 1/3 Paper 1/3 1/3 Stone Player A
5. 5. Z Scissors Paper StoneAND: xOR: + 1/3 Scissors Draw 1/3 x 1/3 = 1/9 AND Scissors Paper A Wins 1/3 x 1/3 = 1/9 1/3 1/3 Stone B Wins 1/3 x 1/3 = 1/9 1/3 OR 1/3 Scissors B Wins 1/3 x 1/3 = 1/9 Paper Paper Draw 1/3 x 1/3 = 1/9 1/3 1/3 1/3 Stone A Wins 1/3 x 1/3 = 1/9 1/3 1/3 Scissors A Wins 1/3 x 1/3 = 1/9 Stone B Wins 1/3 x 1/3 = 1/9 1/3 Paper 1/3 Stone Draw 1/3 x 1/3 = 1/9 Player A Player B 9/9P(A Wins) = /9 + 1/9 + 1/9 1 P(B Wins) =/9 + 1/9 + 1/9 1 P(Draw) = 1/3 = 3/9 = 1/3 = 3/9 = 1/3
6. 6. Two Dice
7. 7. First Die Second Die Six Six Not six Six Not six Not six
8. 8. PROBABILITIESFirst Die Second Die 1 6 Six 1 6 Six 5 Not six 1 6 Six 6 5 Not Six 6 5 Not six 6
9. 9. PROBABILITIESFirst Die Second Die 1 1 1 1 Six 6 6 36 6 1 6 Six 1 5 5 5 Not six 6 6 36 1 6 Six 5 1 5 6 6 6 36 Not 5 Six 6 Not six 5 5 25 5 6 6 36 6
10. 10. Colin has a tin of sweets:6 chocolates and 4 mintsProduce a tree diagram toshow the probabilities oftaking one sweet followed byanother sweet.What is the probability oftaking two of the same type?
11. 11. First Sweet Second Sweet Chocolate Chocolate Mint Chocolate Mint Mint
12. 12. PROBABILITIESFirst sweet Second sweet 6 5 30 5 C 10 9 90 6 9 10 C 4 6 4 24 10 9 90 9 M 6 C 4 6 24 9 10 9 90 4 M 10 3 4 3 12 9 M 10 9 90
13. 13. What is the probability of taking two of the same type? 6 5 30Chocolate and chocolate = 10 9 90 4 3 12 Mint and mint = 10 9 90 30 12 42 So two of the same = 90 90 90
14. 14. TaskMake up a story of your ownDraw a tree diagramLabel all possible outcomes