Creative
Thinker
Effective
Participator
Independent
Enquirer
Reflective
Learner
Self
Manager
Team
Worker
Which ones are you using?
PLT Skills
LESSON OBJECTIVES
Always aim
high!
We are learning to:
- Enhance Mathematical basic skills knowledge.
(Which PLT skills?)
- Accurately calculate the probability of independent
events. (Grades B-A)
Where are we in
our journey?
AUTHOR
www.mistrymaths.co.uk
Real life
cross/curricular
links?
Creative
Thinker
PLT Skills
Effective
Participator
Independent
Enquirer
Reflective
Learner
LEARNING JOURNEY
Self
Manager
Team
Worker
Which ones are you using?
Creative
Thinker
Effective
Participator
PLT Skills
Independent
Enquirer
STARTER
Reflective
Learner
Self Manager
Team
Worker
Which ones are you using?
TASK
1) Find the median 2) x2 - 2x
of: 3, 6, 9, 12
= 7.5
4)
= 5
3) Expand -5(-4x - 3)
When x = -3
= (-3) 2 -2 X -3 = 15
5) Calculate 112
6) Find the LCM of 8
= 11 x 11 = 121
and 4.
= 8
7) 50% of 40miles 8) Simplify:
= 20miles
EXTENSION
= 20x + 15
8e + 6y – 9e + 7y
= -e + 13y
9m
9) Solve:
6(x + 8) = 60
6x + 48 = 60
= 12
6x
x
=2
Calculate the area of the trapezium
2m
Area =
11m
(a + b)h Area =
(9 + 11)2 Area = 20m 2
Creative
Thinker
Effective
Participator
Independent
Enquirer
Reflective
Learner
INDEPENDENT EVENTS
PLT Skills
Self
Manager
Team
Worker
Which ones are you using?
Independent Events →
OR → +
AND → X
EXAMPLE
The chance that Ashley hits a target with an arrow is . He has two shots at the target.
What is the probability of each of these outcomes?
(b) Hits target only once
(c) Hits target at least once
(a) Hits target both times
P(Hits target once only)
P(Hits both times)
This is the
same as
This is the
same as
P(1st hits and 2nd hits)
P(1st hits,2nd misses or 1st
x
x
P(Hits both times) =
P(Hits at least once)
1
16
+
misses,2nd hits)
This is the
same as
x
3
3
+
16
16
6
P(Hits target once only) =
16
P(Hits target once only) = 3
8
Worked
out in (a)
Worked
out in (b)
+
+
=
Creative
Thinker
Effective
Participator
Independent
Enquirer
Reflective
Learner
Self
Manager
Team
Worker
PLT Skills INDEPENDENT EVENTS Which ones are you using?
TASK (GRADE B)
1) Alf tosses a coin twice. The coin is biased so it has a probability of two-thirds of landing on a
head. What is the probability that he gets: (a) two heads (b) a head and a tail (in any order)?
2) Bernice draws a card from a pack of cards, replaces it, shuffles the pack and then draws
another card. What is the probability that the cards are:
(a) both Aces
(b) an Ace and a King (in any order)?
3) A dice is thrown twice. What is the probability that both scores are:
(a) even
(b) one even and one odd (in any order)?
4) I throw a dice three times. What is the probability of getting three sixes?
5) A bag contains 15 white beads and 10 black beads. I take out a bead at random, replace it and
take out another bead. What is the probability that: (a) both beads are black
(b) one bead is black and the other white (in any order)?
6) The probability that I am late for work on Monday is 0.4. The probability that I am late on
Tuesday is 0.2. What is the probability of each of the following outcomes?
(a) I am late for work on Monday and Tuesday.
(b) I am late for work on Monday and on time on Tuesday.
(c) I am on time on both Monday and Tuesday.
= 0.48
Creative
Thinker
Effective
Participator
Independent
Enquirer
Reflective
Learner
Self
Manager
Team
Worker
PLT Skills INDEPENDENT EVENTS Which ones are you using?
EXTENSION (GRADE A)
1) Ronda has to take a three-part language examination paper. The first part is speaking. She has
a 0.7 chance of passing this part. The second part is listening. She has a 0.6 chance of passing
this part. The third part is writing. She has a 0.8 chance of passing this part.
(a) If she passes all three parts, her father will give her £20. What is the probability that she gets
the money?
= 0.336
(b) If she passes two parts only, she can resit the other part. What is the chance she will have to
resit?
= 0.452
(c) If she fails all three parts, she will be thrown off the course. What is the chance she is thrown
off the course?
= 0.024
2) Roy regularly goes to Bristol by train. The probability of the train arriving in Bristol late is 0.05.
The probability of it raining in Bristol is 0.8. What is the probability of:
(a) Roy getting to Bristol on time and it not raining
(b) Roy travelling to Bristol five days in a row and not being late at all
= 0.19
= 0.77
(c) Roy travelling to Bristol three days is a row and it raining every day?
= 0.512
3)What is the probability of rolling the same number on a dice five times in a row?
4) Explain why picking a red card from a pack of cards and picking a King from a pack of cards
are not independent events. Red cards can also be kings so it becomes dependent
Creative
Thinker
PLT Skills
Effective
Participator
Independent
Enquirer
Reflective
Learner
INDEPENDENT EVENTS
Self
Manager
Team
Worker
Which ones are you using?
MINI-PLENARY ACTIVITY
Watch the roulette video. What is the probability of them winning?
http://www.youtube.com/watch?v=5GGnHHjG1Uc
AMERICAN ROULETTE
18
38
38 numbers
x
18
38
P(Winning) =
x
18
38
x
18
38
x
18
38
= 0.02 (2d.p.)
Creative
Thinker
PLT Skills
Effective
Participator
Independent
Enquirer
DISCOVERY
Reflective
Learner
Self
Manager
Team
Worker
Which ones are you using?
LINK BACK TO OBJECTIVES
- Accurately calculate the probability of
independent events.
What grade
are we
working at?
Creative
Thinker
Effective
Participator
Independent
Enquirer
Reflective
Learner
Self
Manager
Team
Worker
PLT Skills INDEPENDENT EVENTS Which ones are you using?
PLENARY ACTIVITY – EXAM QUESTION (GRADE B)
Sam has two bags of marbles. Bag A contains 9 red marbles and 6 green marbles.
Bag B contains 3 red marbles and 7 green marbles. Sam rolls a fair six-sided dice
once. If she rolls a six she takes a marble from bag A. If she does not roll a six she
takes a marble from bag B. Calculate the probability that Sam chooses a red marble.
P(6) =
1
6
P(Not 6) =
BAG A
Bag A
5
6
Bag B
BAG B
P(Red) = (Rolling a 6, Red from bag A)
1 X 9
5 X 3
P(Red) =
+
6
6
15
10
9
7
15
P(Red) =
+
=
90
20
60
+
(Not rolling a 6, Red from bag B)
(3 marks)
What have you learnt?
Draw your brain
In your brain, write or draw everything you can remember about accurately
calculating the probability of independent 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
Thinker
Creative
Entrepreneur
Independent
Learner
Reflective
Learner
Responsible
Citizen
Team
Worker
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
www.mistrymaths.co.uk
I fully
understand
Positive
Thinker
Creative
Entrepreneur
Independent
Learner
Reflective
Learner
Responsible
Citizen
Team
Worker
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.
www.mistrymaths.co.uk