1. Car Race – Linear Sequences
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Car Race – Linear Sequences

2. Tree Diagrams Independent Events
19 February 2019
Tree Diagrams
Independent Events

3. Which is bigger? 1 10 1
100 1 20 1
1000

4. Leicester winning the league last season.1 5
Chips for lunch.
Leicester winning the league last season. 1
500 1
3,000,000
Winning the lottery

5. Alice picks a button.
Josh picks a button. R Y R R R R R R R R

6. Results Alice Pick Josh Pick Y YY Y R YR Y RY R R RR 1 10 1 10 1 10 1
100 Y YY x = Y 1 10 9 10 1 10 9 10 9
100 R YR x = 1 10 9 10 1 10 9
100 Y 9 10 RY x = R 9 10 9 10 9 10 81
100 R RR x =

7. We know probabilities must add up to 1.
What is the probability of choosing any blue button? 6 10
0.6
What is the probability of choosing any red button? 4 10
0.4 B
P(BLUE BUTTON) = 6 10 6 10
We know probabilities must add up to 1.
START 4 10 R
P(RED BUTTON) = 4 10

8. We know probabilities must add up to 1.
What is the probability of choosing any blue button? 6 10
What is the probability of choosing any red button? 4 10 B
P(BLUE BUTTON) = 6 10 6 10
We know probabilities must add up to 1.
START 4 10 R
P(RED BUTTON) = 4 10

10. Complete the Tree Diagram in your books
What is the probability of choosing any yellow button? 7 10
0.7
Complete the Tree Diagram
in your books Y
P(YELLOW BUTTON) = 7 10 7 10
START 3 10 B
P(RED BUTTON) = 3 10

11. Complete the Tree Diagram in your books
What is the probability of choosing any yellow button? 7 10
Complete the Tree Diagram
in your books Y
P(YELLOW BUTTON) = 7 10 7 10
START 3 10 B
P(RED BUTTON) = 3 10

13. Complete a Tree Diagram on your whiteboard.
Use fractions or decimals or both. B
P(BLACK BUTTON) = 5 10 5 10
START 5 10 Y
P(PINK BUTTON) = 5 10

14. Complete a Tree Diagram on your whiteboard.
Use fractions or decimals or both. Y
P(YELLOW BUTTON) = 9 10 9 10
START 1 10 P
P(PINK BUTTON) = 1 10

15. To draw one-stage tree diagrams. To draw complex tree diagrams.
19 February 2019
Tree Diagrams
To draw one-stage tree diagrams.
To draw complex tree diagrams.
Keywords: probability, chance, likely, unlikely, expected

16. Tree Diagrams often show one event followed by another.
- one dice followed by a second dice
- one coin followed by a second coin
- one day followed by another day
- one pick from a bag followed by a second pick

17. We will pick a button
– then put it back –
then pick another.

18. We MULTIPLY the probabilities.
Results
2nd Pick 2 10 2 10 2 10 4
100 B BB x =
1st Pick 2 10 B
1st Pick Black
2nd Pick Black
We MULTIPLY the probabilities. 8 10 2 10 8 10 16
100 BY x = Y 2 10 8 10 2 10 16
100 8 10 YB x = B Y 8 10 8 10 8 10 64
100 Y YY x =

19. We will pick a button
– then put it back –
then pick another.

20. Results 2nd Pick PP 1st Pick PY YP YY 4 10 4 10 4 10 16 100 P x = 4 1024
100 PY x = Y 4 10 6 10 4 10 24
100 6 10 P YP x = Y 6 10 6 10 6 10 36
100 Y YY x =

23. Results 2nd Pick BB 1st Pick BY YB YY 3 10 3 10 3 10 9 100 B x = 3 107 10 3 10 7 10 21
100 BY x = Y 3 10 7 10 3 10 21
100 7 10 B YB x = Y 7 10 7 10 7 10 49
100 Y YY x =

25. Results 2nd Pick BB 1st Pick BY YB YY 4 10 4 10 4 10 16 100 B x = 4 1024
100 BY x = Y 4 10 6 10 4 10 24
100 6 10 B YB x = Y 6 10 6 10 6 10 36
100 Y YY x =

26. 1st Pick
2nd Pick
Results
Template Available!

27. Hand up when you’re finished so I can check and give you a challenge!

28. 1st Pick, then the button goes back.
10 buttons
8 buttons
3 colours
Draw a Tree Diagram:
1st Pick, then the button goes back.
2nd Pick.
Results.

30. Jo randomly picks one button, puts it back, then picks another button.
10 buttons:
4 Black
6White
7 buttons:
3 Black
4 White
Jo randomly picks one button, puts it back, then picks another button.
Draw a Tree Diagram to show the probabilities.
Mo randomly picks one button, puts it back, then picks another button.
Draw a Tree Diagram to show the probabilities.

32. What’s wrong? What’s the answer?

33. We will pick a button
– then put it back –
then pick another.

34. Results 2nd Pick RR 1st Pick RY YR YY 4 10 4 10 4 10 8 10 R x = 4 10 R5 10 4 10 5 10 20
100 RY x = Y 4 10 6 10 4 10 24
100 6 10 R YR x = Y 6 10 6 10 6 10 36 20 Y YY x =

35. ‘AND Rule’
P (A and B) = P(A) x P(B)
‘OR Rule’
P (A or B) = P(A) + P(B)

36. What is the probability of HH? TT? One H and one T?
Tree Diagram: Coins
1st Coin
2nd Coin
Results 1 2 1 2 1 2 1 4 HH x = H 1 2 H 1 2 1 2 1 4 1 2 HT x = T
START 1 2 1 2 1 2 1 4 TH x = 1 2 H T 1 2 1 2 1 4 1 2 TT x = T
What is the probability of HH? TT? One H and one T?

37. 1st Roll 2nd Roll Results 6 66 6 6,N6 6 N6,6 N6,N6 1 6 1 6 1 6 1 36 x
Tree Diagram: DICE, 6 or NOT 6
1st Roll
2nd Roll
Results 1 6 1 6 1 6 1 36 6 66 x = 1 6 6
NOT 6 1 6 5 6 5 36 5 6 x =
6,N6
START 1 6 5 6 1 6 5 36 6
N6,6 x = 5 6
NOT 6
NOT 6 5 6 5 6 25 36 5 6
N6,N6 x =
What is the probability of getting no sixes? Only 1 six?