Probabilistic Analysis with Tree Diagrams for Ball Selections

Explore the concept of tree diagrams in probability by solving problems related to the selection of colored balls from bags without replacement. Understand the probabilities associated with picking different colored balls in multiple scenarios involving various numbers of picks and colored balls per bag.

• Tree diagrams
• Probability analysis
• Ball selections
• Colored balls
• Without replacement

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Uploaded on Sep 20, 2024 | 0 Views

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1. Tree Diagrams: Tree Diagrams: no replacement no replacement version 2 version 2 Silent Teacher Intelligent Practice Your Turn Narration Practice

2. Worked Example Your Turn There are 4 yellow and 5 red balls in a bag. A ball is picked and not replaced. A second ball is then picked. Complete the tree diagram showing the probabilities on each branch. There are 3 yellow and 5 red balls in a bag. A ball is picked and not replaced. A second ball is then picked. Complete the tree diagram showing the probabilities on each branch. @mrbartonmaths

3. The numbers of coloured balls in a bag and the number of picks are given in each question. Each time a ball is picked, it is not replaced. Draw a tree diagram showing the probabilities on each branch 1. 5 yellow and 5 red balls Two picks 8. 3 yellow and 6 red balls Two picks 15. 4 yellow, 7 red and 3 green balls Three picks 2. 4 yellow and 4 red balls Two picks 9. 3 yellow and 6 red balls Three picks 3. 4 yellow and 3 red balls Two picks 10. 3 yellow and 7 red balls Three picks 4. 3 yellow and 4 red balls Two picks 11. 2 yellow and 7 red balls Three picks 5. 2 yellow and 5 red balls Two picks 12. 2 yellow and 7 red balls Two picks 6. 1 yellow and 6 red balls Two picks 13. 2 yellow, 7 red and 3 green balls Two picks 7. 1 yellow and 2 red balls Two picks 14. 4 yellow, 7 red and 3 green balls Two picks @mrbartonmaths

4. 3. 4 yellow and 3 red balls Two picks 1. 5 yellow and 5 red balls Two picks 3 6 4 9 4 7 5 10 3 6 5 9 4 6 5 9 3 7 5 10 2 6 4 9 4. 3 yellow and 4 red balls Two picks 2. 4 yellow and 4 red balls Two picks 2 6 3 7 3 7 4 8 4 6 4 7 3 6 4 7 4 7 4 8 3 6 3 7

5. 7. 1 yellow and 2 red balls Two picks 5. 2 yellow and 5 red balls Two picks 0 2 1 6 1 3 2 7 2 2 5 6 1 2 2 6 2 3 5 7 1 2 4 6 8. 3 yellow and 6 red balls Two picks 6. 1 yellow and 6 red balls Two picks 2 8 0 6 3 9 1 7 6 8 6 6 3 8 1 6 6 9 6 7 5 8 5 6

6. 9. 3 yellow and 6 red balls Three picks 1 7 Yellow Yellow 2 8 Red 6 7 2 7 3 9 Yellow Yellow 6 8 Red 5 7 Red 2 7 Yellow Yellow 3 8 6 9 Red Red 5 7 3 7 Yellow 5 8 Red Red 4 7

7. 10. 3 yellow and 7 red balls Three picks 1 8 Yellow Yellow 2 9 Red 7 8 2 8 3 Yellow Yellow 10 7 9 Red 6 8 Red 2 8 Yellow Yellow 3 9 7 10 Red Red 6 8 3 8 Yellow 6 9 Red Red 5 8

8. 11. 2 yellow and 7 red balls Three picks 0 7 Yellow Yellow 1 8 Red 7 7 1 7 2 9 Yellow Yellow 7 8 Red 6 7 Red 1 7 Yellow Yellow 2 8 7 9 Red Red 6 7 2 7 Yellow 6 8 Red Red 5 7

9. 12. 2 yellow and 7 red balls Two picks 1 8 2 9 7 8 2 8 7 9 6 8

10. 13. 2 yellow, 7 red and 3 green balls Two picks Y 1 11 7 R 11 3 Y 11 2 G 2 12 Y 11 7 6 12 11 R R 3 G 11 2 3 Y 11 12 G 7 11 R 2 11 G

11. 14. 4 yellow, 7 red and 3 green balls Two picks Y 3 13 7 R 13 3 Y 13 4 G 4 14 Y 13 7 7 13 14 R R 3 G 13 4 3 Y 13 14 G 7 13 R 2 13 G