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PLT Skills
LESSON OBJECTIVES
Always aim
high!
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*)
Where are we in
our journey?
AUTHOR
www.mistrymaths.co.uk
Real life
cross/curricular
links?
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PLT Skills
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LEARNING JOURNEY
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PLT Skills
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STARTER
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TASK
1) Find the median 2) x2 - 7
of: 2, 4, 7, 11
= 5.5
3) Expand 5(-3x + 2)
When x = -6
= (-6) 2 - 7 = 29
4) Write the value 5) Calculate
5 cubed.
= 125
49
= 7 and -7
7) 25% of 36 miles 8) Simplify:
=
=9
EXTENSION
5e + 8y – 9e – 7y
= -4e + y
7m
= -15x + 10
6) Find the HCF of
18 and 30.
= 6
9) Solve:
8(x + 4) = 56
8x + 32 = 56
= 24
8x
x
=3
Calculate the area of the trapezium
4m
Area =
11m
(a + b)h Area =
(7 + 11)4 Area = 36m 2
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PROBABILITY TREES
EXAMPLE
6
42 are blue
48 and8seven of
Hubert has
10 coloured
counters
in a bag.
Three
of
the
counters
P(The
same
colour)
= P(B,B)
+ P(G,G) = 90 + 90 =
=
90and notes
15 the
the counters are green. He removes a counter at random from the bag
colour and does not replace it. He then chooses a second
21 Record
21 counter.
42 the
7
P(BG
in any
order)
= P(B,G)
P(G,B)
= 90 +of90
=
information
on a tree
diagram
and work+out
the probabilities
the =
different
outcomes.
90
15
ALWAYS MULTIPLY THE BRANCHES
FIRST PICK
SECOND PICK
3
2
6
2
X
=
Blue P(B,B) = 10
9
90
9
3
10
7
10
Blue
3
9
COUNTERS HAVE NOT
3
7
21
BEEN=REPLACED
SO
Green P(B,G)
X
= 90
10
9
THE PROBABILITY
7
3
21
Blue P(G,B)
DOES CHANGE
X ON =THE
=
10
9
90
SECOND PICK
6
9
7
6
42
X
Green P(G,G) =
10
9 = 90
7
9
Green
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PROBABILITY TREES
TASK (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.
First Pick
Second Pick
17
29
18
30
12
30
Milk
P(milk and milk) =
Milk
P(Milk and Milk) =
P(milk and dark) =
12
29
18
29
11
29
18 12 216
x

30 29 870
Dark P(Milk and Dark) =
P(dark and milk) =
Milk
Dark
12 18 216
x

30 29 870
P(Dark and Milk) =
P(dark and dark) =
Dark
18 17 306
x

30 29 870
12 11 132
x

30 29 870
P(Dark and Dark) =
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PROBABILITY TREES
TASK (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.
FIRST PICK
SECOND PICK
1
4
2
5
3
5
2
20
6
(b) P(Red,Red) =
20
(a) P(Blue,Blue) =
ALWAYS MULTIPLY THE BRANCHES
2
1
2
X
P(B,B)
=
Blue
5
4 = 20
Blue
3
4
2
4
COUNTERS HAVE NOT
2
3
BEEN=REPLACED
SO 6
Red
X
P(B,R)
=
5
4
20
THE PROBABILITY
3
2
6
DOES CHANGE
ON=THE
Blue P(R,B)
X
=
5
4
20
SECOND
PICK
Red
1
3
2
3
2
6
=
=
X
Red P(R,R) =
10
=
5
4
5
4
20
3
6
6 = 12
(c) P(One blue and one red in any order) =
=
+
10
20
20 20
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PROBABILITY TREES
TASK (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.
FA CUP
ALWAYS MULTIPLY THE BRANCHES
PREMIERSHIP
0.6
Win
P(W,W) = 0.7 x 0.6 = 0.42
Lose
P(W,L) = 0.7 x 0.4 = 0.28
Win
0.7
0.4
0.5
0.3
Win P(L,W) = 0.3 x 0.5 = 0.15
Lose
0.5
Lose P(L,L) = 0.3 x 0.5 = 0.15
Use a tree diagram to find the probability that they win
P(Only one W) = 0.28 + 0.15
(a) the ‘double’ P(Double) = 0.42
(b) only one of them
= 0.43
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PROBABILITY TREES
EXTENSION (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.
(b) All customers were entered into a prize draw.
(a) Complete the tree diagram below:
What is the probability that the winner bought a
Probability
Flat
0·75
Hi-Fi system with a normal screen television?
adds up to
Video
one whole
0.25
Normal
0.0125
0·35
0·75
0·6
Flat
DVD
0.25
Normal
0.05
0·75
Flat
Hi-Fi
0.25
Normal
P(H,N) = 0.05 x 0.25 = 0.0125
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PROBABILITY TREES
EXTENSION (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.
(b) What is the probability Zoe will choose
the same sports activity on both days?
(a) Complete the tree diagram below:
P(Same sport) = 0.25 + 0.16+ 0.01
Probability
adds up to
one whole
= 0.42
P(B,B) = 0.5 x 0.5 = 0.25
0.1
P(D,D) = 0.4 x 0.4 = 0.16
0.1
0.1
0.1
P(N,N) = 0.1 x 0.1 = 0.01
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DISCOVERY
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LINK BACK TO OBJECTIVES
- Accurately draw probability trees for
dependent events and work out
probabilities from this.
What grade
are we
working at?
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PROBABILITY TREES
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PLT Skills
PLENARY ACTIVITY – ROCK, PAPER AND SCISSORS
TASK
Complete a fully labelled tree
diagram to shows the
outcomes of a rock, paper
and scissors game between
two players.
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PROBABILITY TREES
PLENARY ACTIVITY
Player A
Scissors
Player B
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Scissors Draw
1/3 x 1/3 = 1/9
Paper
A Wins 1/3 x 1/3 = 1/9
Stone
B Wins 1/3 x 1/3 = 1/9
Scissors B Wins 1/3 x 1/3 = 1/9
Paper
1/3 x 1/3 = 1/9
Paper
Draw
Stone
A Wins 1/3 x 1/3 = 1/9
Scissors A Wins 1/3 x 1/3 = 1/9
Stone
P(A Wins) = 1/9 + 1/9 + 1/9
= 3/9
= 1/3
Paper
B Wins 1/3 x 1/3 = 1/9
Stone
Draw
1/3 x 1/3 = 1/9
P(B Wins) = 1/9 + 1/9 + 1/9 P(Draw) = 1/3
= 3/9
= 1/3
What have you learnt?
Draw your brain
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.
Where are we
in our
journey?
What grade
are we
working at?
Positive
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Enterprise Skills SELF ASSESSMENT Which ones are you using?
Plenary Activity
How well do you understand the task?
.
I don’t
understand
I nearly
understand
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I fully
understand
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Enterprise Skills SELF ASSESSMENT Which ones are you using?
Plenary Activity
WWW (What Went Well)
EBI (Even Better If)
On your post it
notes…
Think about how you
can improve your
work.
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