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

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 + 4When x = -5

Find the mean of: 2, 3, 5, 10

Expand 4(-4x + 5)

Write the value of pi to 2d.p.

5)

Calculate 6)

Find the LCM of 6 and 4.

7)

75% of 24 miles 8)

Simplify:5e + 6y – 7e – 5y

9)

Solve:7(x + 3) = 56

2

16

9m

6m

3mCalculate the area of the trapezium

= = 5 (-5) + 42 = 29== -16x + 20

= 3.14 = 4 and -4 = 12

= = 18= -2e + y 7x + 21 = 56

7x = 35x = 5

Area = (a + b)h Area = (6 + 9)3 Area = 22.5cm 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 before replacing 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 BEEN REPLACED SO THE PROBABILITY DOES

NOT CHANGE ON THE SECOND PICK

310

710

310

710

P(B,B) =

ALWAYS MULTIPLY THE BRANCHES

103

X103

= 1009

P(B,G) =103

X107

= 10021

P(G,B) =107

X103

= 10021

P(G,G) =107

X107

= 10049

P(The same colour) = P(B,B) + P(G,G) =1009

+10049

= 10058

= 5029

P(BG in any order) = P(B,G) + P(G,B) = 10021

+10021

= 10042

= 5021

PROBABILITY TREES

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Reflective Learner Which ones are you

using?PLT SkillsTASK (GRADE B)

Fill in the probability tree below to display the outcomes of flipping a fair coin twice:

2nd 1st

H

……

…...

…...

…...

T

…....

…....

…....

…....

…....

P(H,H)=…………………

P(H,T)=………………....

P(T,H)=………………....

P(T,T)=………………….

Flip Flip

1)

1 2

T

H

T

H

21

21

21

21

21

21

X 21

= 41

21

X 21

= 41

21

X 21

= 41

21

X 21

= 41

PROBABILITY TREES

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Self Manager

Independent Enquirer

Creative Thinker

Team Worker

Reflective Learner Which ones are you

using?PLT SkillsTASK (GRADE B)2)

black

green

First Choice Second Choice

59

black

green

black

green

49 4 5

P(black and green) =9 9

2081

x

5 5P(green and green) =

9 92581

x

49

59

49

59

4 4P(black and black) =

9 91681

x

5 4P(green and black) =

9 92081

x

Rebecca has nine coloured beads in a bag. Four of the beads are black and the rest are green. She removes a bead at random from the bag and notes the colour before replacing it. She then chooses a second bead. (a) Draw a tree diagram showing all possible outcomes. (b) Calculate the probability that Rebecca chooses: (i) 2 green beads (ii) A black followed by a green bead (iii) The same colour.

P(same colour) = 8116

+ 8125 =

8141

P(E,E) =

PROBABILITY TREES

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Independent Enquirer

Creative Thinker

Team Worker

Reflective Learner Which ones are you

using?PLT SkillsTASK (GRADE B)3)

(a) Complete a tree diagram to show all the probabilities of obtaining even and odd numbers.

(b) Calculate the probability of spinning two numbers which multiply to given an even number.

Even

Odd

2 5

3 5

Even

Odd

Even

Odd

2 5

3 5

2 5

3 5

52

X 52

= 254

P(E,O) = 52

X 53

= 25 6

P(O,E) = 53

X 52

= 25 6

P(O,O) = 53

X 53

= 259

P(EE) + P(EO) + P(OE) P(Spinning two numbers which multiply to make an even) = = + + =

PROBABILITY TREES

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Self Manager

Independent Enquirer

Creative Thinker

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Reflective Learner Which ones are you

using?PLT SkillsEXTENSION (GRADE A)1) Peter and Becky run a race and play a tennis match. The probability that Peter wins

the race is 0.4. The probability that Becky wins the tennis is 0.7. (a) Complete the tree diagram below. (b) Use your tree diagram to calculate (i) the probability that Peter wins both events. (ii) The probability that Becky loses the race but wins at tennis.

Becky Win

Becky Win

Peter Win

Becky Win

Race TennisPeter Win

Peter Win

0.40.7

0.6

0.3

0.3

0.7

0.4 x 0.3 = 0.12

0.4 x 0.7 = 0.28

0.6 x 0.3 = 0.18

0.6 x 0.7 = 0.42

P(Win and Win) for Peter = 0.12

P(Lose and Win) for Becky = 0.28

PROBABILITY TREES

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Self Manager

Independent Enquirer

Creative Thinker

Team Worker

Reflective Learner Which ones are you

using?PLT SkillsEXTENSION (GRADE A)2) Peter has ten coloured cubes in a bag. Three of the cubes are red and seven are

blue. He removes a cube at random from the bag and notes the colour but does not replace it. He then chooses a second cube at random. Record the information in a tree diagram.

red

blue

First ChoiceSecond Choice

3 2P(red and red) =

10 96

90x

710

red

blue

red

blue

310 3 7

P(red and blue) =10 9

2190

x

7 3P(blue and red) =

10 92190

x

7 6P(blue and blue) =

10 94290

x

29

79

39

69

DISCOVERY

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Reflective Learner Which ones are you

using?PLT Skills

LINK BACK TO OBJECTIVES

- Accurately draw probability trees for independent 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 – GRADE B EXAMINATION QUESTION

Weather records are kept in a town called Snowville. They show that in a typical April it snows on 20 days out of the 30 days in the month.

PROBABILITY TREES

(a) Complete a fully labelled tree diagram showing the probabilities of it snowing or not snowing on the first two Sundays in April in Snowville.

(b) Calculate the probability that it snows on only one of these two Sundays. You must show your working.

(4 marks)

(3 marks)

FIRST SUNDAY SECOND SUNDAY

SNOW

NOT SNOW

SNOW

NOT SNOWSNOW

NOT SNOW

=

=

P(S,S) = 32

X 32

= 94

P(S,NS) = 32

X 31

= 92

P(NS,S) = 31

X 32

= 92

P(NS,NS) = 31

X 31

= 91

P(S,NS or NS, S) = 92

+ 92

= 94

Draw your brain

What have you learnt?

In your brain, write or draw everything you can remember about drawing probability trees for independent 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