1. Tree Diagrams Objective: To calculate probability using a tree diagram. Lesley Hall @ Soar Valley College Five balls are put into a bag. Three are red. Two are blue. A ball is chosen at random and replaced. A second ball is then chosen. Draw a tree diagram to show all the possible outcomes and their probabilities.

2. Tree Diagrams Objective: To calculate probability using a tree diagram. Lesley Hall @ Soar Valley College 1 st choice You could either pick out a red ball… … or a blue ball. R B P(red ball) = 3 5 3 5 P(blue ball) = 2 5 2 5

3. Tree Diagrams Objective: To calculate probability using a tree diagram. Lesley Hall @ Soar Valley College 1 st choice R B 3 5 2 5 2 nd choice If you chose a red the 1 st time, you can still choose a red or a blue the 2 nd time. R B If you chose a blue the 1 st time, you can still choose a red or a blue the 2 nd time. R B

4. Tree Diagrams Objective: To calculate probability using a tree diagram. Lesley Hall @ Soar Valley College 1 st choice R B 3 5 2 5 2 nd choice R B R B Because we replace the first ball the probabilities will stay the same! 2 5 2 5 3 5 3 5 Notice that on each pair of branches the probabilities add up to 1. 2 5 3 5 += 1

5. Tree Diagrams Objective: To calculate probability using a tree diagram. Lesley Hall @ Soar Valley College 1 st choice R B 3 5 2 5 2 nd choice R B R B 2 5 2 5 3 5 3 5 2 5 List the outcomes … R R R B B R B B

6. Tree Diagrams Objective: To calculate probability using a tree diagram. Lesley Hall @ Soar Valley College 1 st choice R B 3 5 2 5 2 nd choice R B R B 2 5 2 5 3 5 3 5 2 5 RR RBRB BRBR BB …and work out the probabilities. 3 5 3 5 + = 9 25 3 5 2 5 + = 6 2 5 3 5 + = 6 2 5 2 5 + = 4 Finally check that your probabilities add up to 1.

7. Tree Diagrams Objective: To calculate probability using a tree diagram. Lesley Hall @ Soar Valley College 1 st choice R B 3 5 2 5 2 nd choice R B R B 2 5 2 5 3 5 3 5 2 5 RR RBRB BRBR BB 3 5 3 5 + = 9 25 3 5 2 5 + = 6 2 5 3 5 + = 6 2 5 2 5 + = 4 You can now use your tree diagram to answer questions.