We are learning to:- Enhance Mathematical basic skills knowledge. (Which PLT skills?) -Accurately draw probability trees for dependent events and work out probabilities from this. (Grade A*)

Always aim high!LESSON OBJECTIVES

Effective Participator

Self Manager

Independent Enquirer

Creative Thinker

Team Worker

Reflective Learner

PLT SkillsWhich ones are you

using?

AUTHORWhere are we in

our journey?

Real life cross/curricular

links?www.mistrymaths.co.uk

LEARNING JOURNEY

Effective Participator

Self Manager

Independent Enquirer

Creative Thinker

Team Worker

Reflective Learner Which ones are you

using?PLT Skills

STARTER

Effective Participator Self ManagerIndependent

EnquirerCreative Thinker

Team Worker

Reflective Learner Which ones are you

using?PLT Skills

EXTENSION

TASK

1) 2) 3)

4)

x - 7When x = -6

Find the median of: 2, 4, 7, 11

Expand 5(-3x + 2)

Write the value 5 cubed.

5)

Calculate 6)

Find the HCF of 18 and 30.

7)

25% of 36 miles 8)

Simplify:5e + 8y – 9e – 7y

9)

Solve:8(x + 4) = 56

2

49

11m

7m

4mCalculate the area of the trapezium

= 5.5 (-6) - 72 = 29== -15x + 10

= 125 = 7 and -7 = 6

= = 9= -4e + y 8x + 32 = 56

8x = 24x = 3

Area = (a + b)h Area = (7 + 11)4 Area = 36m 2

Hubert has 10 coloured counters in a bag. Three of the counters are blue and seven of the counters are green. He removes a counter at random from the bag and notes the colour and does not replace it. He then chooses a second counter. Record the information on a tree diagram and work out the probabilities of the different outcomes.

PROBABILITY TREES

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Reflective Learner Which ones are you

using?PLT SkillsEXAMPLE

Blue

Green

310

FIRST PICK

710

SECOND PICK

Blue

Green

Blue

Green

COUNTERS HAVE NOT BEEN REPLACED SO

THE PROBABILITY DOES CHANGE ON THE

SECOND PICK

2 9

7 9

3 9

6 9

P(B,B) =

ALWAYS MULTIPLY THE BRANCHES

103

X 92

= 906

P(B,G) =103

X 97

= 9021

P(G,B) =107

X 93

= 9021

P(G,G) =107

X 9

6= 90

42

P(The same colour) = P(B,B) + P(G,G) = 906

+ 9042

= 9048

= 15 8

P(BG in any order) = P(B,G) + P(G,B) = 9021

+ 9021

= 9042

= 15 7

PROBABILITY TREES

Effective Participator

Self Manager

Independent Enquirer

Creative Thinker

Team Worker

Reflective Learner Which ones are you

using?PLT SkillsTASK (GRADE A*)1) Lucy has a box of 30 chocolates. 18 are milk chocolate and

the rest are dark chocolate. She takes a chocolate at random from the box and eats it. She then chooses a second.

Draw a tree diagram to show all the possible outcomes.

Milk

First Pick Second Pick

1230

Dark

P(Milk and Milk) =

P(Milk and Dark) =

P(Dark and Milk) =

P(Dark and Dark) =

1830

Dark

Milk

Dark

Milk

1729

1229

1829

1129

18 17P(milk and milk) =

30687030 29

x

18 12P(milk and dark) =

21687030 29

x

12 18P(dark and milk) =

21687030 29

x

12 11P(dark and dark) =

13287030 29

x

PROBABILITY TREES

Effective Participator

Self Manager

Independent Enquirer

Creative Thinker

Team Worker

Reflective Learner Which ones are you

using?PLT SkillsTASK (GRADE A*)2)Jimmy has five coloured counters in a bag. Two of the counters are

blue and the rest are red. He removes a counter at random from the bag and notes the colour but does not replace it. He then chooses a second counter. Draw a tree diagram showing all possible outcomes.

(a) P(Blue,Blue) = (b) P(Red,Red) = (c) P(One blue and one red in any order) =

Blue

Red

2 5

FIRST PICK

3 5

SECOND PICK

Blue

Red

Blue

Red

COUNTERS HAVE NOT BEEN REPLACED SO

THE PROBABILITY DOES CHANGE ON THE

SECOND PICK

1 4

3 4

2 4

2 4

P(B,B) =

ALWAYS MULTIPLY THE BRANCHES

52

X 41

= 202

P(B,R) = 52

X 43

= 20 6

P(R,B) = 53

X 42

= 20 6

P(R,R) = 53

X 4

2= 20

6 202

= 10

1

206

= 10

3 20 6

+ 20 6 =

2012

= 5 3

PROBABILITY TREES

Effective Participator

Self Manager

Independent Enquirer

Creative Thinker

Team Worker

Reflective Learner Which ones are you

using?PLT SkillsTASK (GRADE A*)3)The probability Manchester City will win the Premiership is 0.7. If they do, the

probability they will go on to win the F.A. Cup is 0.6. But if they don’t, it’s only 0.5. Draw a tree diagram to represent this information.

Use a tree diagram to find the probability that they win(a) the ‘double’ (b) only one of them

Win

Lose

0.7

PREMIERSHIP FA CUP

Win

Lose

Win

Lose

P(W,W) =

ALWAYS MULTIPLY THE BRANCHES

P(W,L) =

P(L,W) =

P(L,L) =

0.3

0.6

0.4

0.5

0.5

0.7 x 0.6 = 0.42

0.7 x 0.4 = 0.28

0.3 x 0.5 = 0.15

0.3 x 0.5 = 0.15

P(Double) = 0.42P(Only one W) = 0.28 + 0.15

= 0.43

PROBABILITY TREES

Effective Participator

Self Manager

Independent Enquirer

Creative Thinker

Team Worker

Reflective Learner Which ones are you

using?PLT SkillsEXTENSION (GRADE A*)1) A shop offers a package where customers can choose either a video player or a DVD player or a

Hi-fi system and either a flat screen or a normal screen television. Over a period of time, 35% of the customers choose a video player and 60% choose a DVD player. The rest choose a Hi-fi system. Independently 75% of the customers choose flat screen televisions.

(a) Complete the tree diagram below: (b) All customers were entered into a prize draw. What is the probability that the winner bought a Hi-Fi system with a normal screen television?

Video

D VD

H i-F i

0 ·35

0 ·75

0 ·75

0 ·75

0 ·6

F la t

N o rm a l

F la t

N o rm a l

F la t

N o rm a l

0.05

Probability adds up to one whole

0.25

0.25

0.25 P(H,N) =0.05 x 0.25 = 0.0125

0.0125

PROBABILITY TREES

Effective Participator

Self Manager

Independent Enquirer

Creative Thinker

Team Worker

Reflective Learner Which ones are you

using?PLT SkillsEXTENSION (GRADE A*)2) Sports activities are held after school. Zoe attends these classes on Monday and Wednesday.

She can choose one of badminton, dance or netball on each day. The probability she chooses badminton is 0.5. The probability she chooses dance is 0.4. Assume Zoe’s choices are independent.

(a) Complete the tree diagram below:(b) What is the probability Zoe will choose the same sports activity on both days?

0.1

Probability adds up to one whole

0.1

0.1

0.1

P(B,B) = 0.5 x 0.5 = 0.25

P(D,D) =0.4 x 0.4 = 0.16

P(N,N) =0.1 x 0.1 = 0.01

P(Same sport) = 0.25 + 0.16+ 0.01=0.42

DISCOVERY

Effective Participator

Self Manager

Independent Enquirer

Creative Thinker

Team Worker

Reflective Learner Which ones are you

using?PLT Skills

LINK BACK TO OBJECTIVES

- Accurately draw probability trees for dependent events and work out probabilities from this.

What grade are we

working at?

Effective Participator

Self Manager

Independent Enquirer

Creative Thinker

Team Worker

Reflective Learner

PLT SkillsWhich ones are you

using?PLENARY ACTIVITY – ROCK, PAPER AND SCISSORS

PROBABILITY TREES

Complete a fully labelled tree diagram to shows the

outcomes of a rock, paper and scissors game between

two players.

TASK

P(Draw) =

Effective Participator

Self Manager

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PLT SkillsWhich ones are you

using?PLENARY ACTIVITY

PROBABILITY TREES

Player AScissors

Paper

Stone

Scissors

Paper

Stone

Scissors

Paper

Stone

Scissors

Paper

Stone

Player BDraw

A Wins

B Wins

B Wins

Draw

A Wins

A Wins

B Wins

Draw

1/9

1/9

1/9

1/9

1/9

1/9

1/9

1/9

1/3 x 1/3 =

1/3 x 1/3 =

1/3 x 1/3 =

1/3 x 1/3 =

1/3 x 1/3 =

1/3 x 1/3 =

1/3 x 1/3 =

1/3 x 1/3 =

1/3 x 1/3 = 1/9

P(A Wins) = 1/9 + 1/9 + 1/9

= 3/9 = 1/3P(B Wins) = 1/9 + 1/9 + 1/9

= 3/9 = 1/31/3

Draw your brain

What have you learnt?

In your brain, write or draw everything you can remember about drawing probability trees for dependent events. It can be a skill or a

reflection, or something else that might be prominent in your brain.

What grade are we

working at?

Where are we in our

journey?

.

How well do you understand the task?

I don’t understand

I nearly understand

I fully understand

Creative Entrepreneur

Responsible Citizen

Independent Learner

Positive Thinker

Team Worker

Reflective Learner

Enterprise Skills Which ones are you using?

SELF ASSESSMENT

Plenary Activity

www.mistrymaths.co.uk

SELF ASSESSMENT

Plenary Activity

On your post it notes…

Think about how you can improve your

work.

WWW (What Went Well)

EBI (Even Better If)

Creative Entrepreneur

Responsible Citizen

Independent Learner

Positive Thinker

Team Worker

Reflective Learner

Enterprise Skills Which ones are you using?

www.mistrymaths.co.uk