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 Participat or Self Manager Independen t Enquirer Creative Thinker Team Worker Reflectiv e Learner PLT Skills Which ones are you using? AUTHOR Where are we in our journey? Real life cross/curric ular links? www.mistrymaths.co.uk
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We are learning to: - Enhance Mathematical basic skills knowledge. (Which PLT skills?) -Accurately draw probability trees for independent events and work.
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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)
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
Effective Participator
Self Manager
Independent Enquirer
Creative Thinker
Team Worker
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
Effective Participator
Self Manager
Independent Enquirer
Creative Thinker
Team Worker
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
Effective Participator
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
Effective Participator
Self Manager
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
Effective Participator
Self Manager
Independent Enquirer
Creative Thinker
Team Worker
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
Effective Participator
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
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 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.