MATHEMATICS Probability – Tree Diagrams, OR and AND.
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Transcript of MATHEMATICS Probability – Tree Diagrams, OR and AND.
![Page 1: MATHEMATICS Probability – Tree Diagrams, OR and AND.](https://reader036.fdocuments.in/reader036/viewer/2022082711/56649f0b5503460f94c1efd6/html5/thumbnails/1.jpg)
MATHEMATICSProbability – Tree Diagrams, OR and AND
![Page 2: MATHEMATICS Probability – Tree Diagrams, OR and AND.](https://reader036.fdocuments.in/reader036/viewer/2022082711/56649f0b5503460f94c1efd6/html5/thumbnails/2.jpg)
Lesson Objectives
•The aim of this powerpoint is to help you…
• complete and interpret tree diagrams
• practice using the OR and AND rules for probability
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Scenarios 1 & 2
• For both of the following scenarios, we are going to have a bag containing 5 red beads and 3 black beads. We are going to take 3 beads out of the bag BUT…
• The first scenario is going to involve re-placing the bead we take out back into the bag each time, so none of the probabilities will change.
• The second scenario is going to involve not replacing the bead(s) in the bag, thus leaving fewer beads in the bag for the next selection…so all the probabilities WILL change.
![Page 4: MATHEMATICS Probability – Tree Diagrams, OR and AND.](https://reader036.fdocuments.in/reader036/viewer/2022082711/56649f0b5503460f94c1efd6/html5/thumbnails/4.jpg)
Scenario 15 red beads, 3 black beads - replacement
1st bead Final Outcomes:
RRR = 5/8 × 5/8 × 5/8 = 125/512
RRB = 5/8 × 5/8 × 3/8 = 75/512
RBR = 5/8 × 3/8 × 5/8 = 75/512
RBB = 5/8 × 3/8 × 3/8 = 45/512
BRR = 3/8 × 5/8 × 5/8 = 75/512
BRB = 3/8 × 5/8 × 3/8 = 45/512BBR = 3/8 × 3/8 × 5/8 = 45/512
BBB = 3/8 × 3/8 × 3/8 = 27/512
5/8
Black
Red
3/8
2nd bead 3rd bead
Black
Red
Black
Red
Black
Red
Black
Red
Black
Red
Black
Red
CHECK: All the probabilities in red add up to 512/512 = 1
5/8
3/8
5/8
3/8
5/8
3/8
5/8
3/8
5/8
3/8
5/8
3/8
![Page 5: MATHEMATICS Probability – Tree Diagrams, OR and AND.](https://reader036.fdocuments.in/reader036/viewer/2022082711/56649f0b5503460f94c1efd6/html5/thumbnails/5.jpg)
Scenario 25 red beads, 3 black beads – NO replacement
1st bead Final Outcomes:
RRR = 5/8 × 4/7 × 3/6 = 60/336
RRB = 5/8 × 4/7 × 3/6 = 60/336
RBR = 5/8 × 3/7 × 4/6 = 60/336
RBB = 5/8 × 3/7 × 2/6 = 30/336
BRR = 3/8 × 5/7 × 4/6 = 60/336
BRB = 3/8 × 5/7 × 2/6 = 30/336BBR = 3/8 × 2/7 × 5/6 = 30/336
BBB = 3/8 × 2/7 × 1/6 = 6/336
5/8
Black
Red
3/8
2nd bead 3rd bead
Black
Red
Black
Red
Black
Red
Black
Red
Black
Red
Black
Red
CHECK: All the probabilities in red add up to 336/336 = 1
4/7
3/7
5/7
2/7
3/6
3/6
4/6
2/6
4/6
2/6
5/6
1/6
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Question 1• What is the probability of pulling out 2 reds and a black
bead (in any order) for each scenario?
• Scenario 1: P(RRB) or P(RBR) or P(BRR)
75/512 + 75/512 + 75/512 = 225/512
• Scenario 1: P(RRB) or P(RBR) or P(BRR)
60/336 + 60/336 + 60/336 = 180/336
![Page 7: MATHEMATICS Probability – Tree Diagrams, OR and AND.](https://reader036.fdocuments.in/reader036/viewer/2022082711/56649f0b5503460f94c1efd6/html5/thumbnails/7.jpg)
Question 2• What is the probability of pulling out 3 beads of the same
colour for each scenario?
• Scenario 1: P(RRR) or P(BBB)
125/512 + 27/512 = 152/512
• Scenario 1: P(RRR) or P(BBB)
60/336 + 6/336 = 66/336
![Page 8: MATHEMATICS Probability – Tree Diagrams, OR and AND.](https://reader036.fdocuments.in/reader036/viewer/2022082711/56649f0b5503460f94c1efd6/html5/thumbnails/8.jpg)
Individual Practice & Notes
• Please work through the worksheet called:
ProbTree-S2.xlsx
• When you have finished this worksheet, ask your teacher to mark your work.
• In your exercise books or on paper, please write up your own notes and examples on tree diagrams. Ensure you include details of how NON-REPLACEMENT affects the probabilities on subsequent branches.
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What next?• If you have completed everything so far and there is still
some time left, then it would be very useful to undertake the following two MyMaths lessons…
• MyMaths > Data > Probability > Venn Diagrams 1
• MyMaths > Data > Probability > Venn Diagrams 2
• BOTH of these MyMaths lessons are useful to ALL students whether or not they did the extension work on tree diagrams and the OR and AND rules.