Transcript Probability experimental calculating level 6 lesson

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Enterprise Skills
LESSON OBJECTIVES
Always aim
high!
We are learning to:
- Enhance our Mathematical learning skills.
(Which Enterprise skills?)
- Accurately calculate the experimental probability of
events occurring. (Level 6)
Where are we in
our journey?
AUTHOR
www.mistrymaths.co.uk
Real life
cross/curricular
links?
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EXAMPLE
DITDIONA can be rearranged to make ADDITION
TASK
Work out the following Mathematical anagrams:
LESHETORTIC
Theoretical
REXLAPEIMENT
Experimental
LITAR
Trial
EXTENSION
Develop your own Mathematical anagrams as above as a
creative entrepreneur.
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STARTER
TASK
1) Give an example of an event
which is certain
Square has 4 right angles
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EXTENSION
1) Write 36 as product of
prime factors.
36
Others?
2) Work out angle y below:
6
105°
y
25° 50°
3) A square has how many lines of
symmetry? Draw them on.
1
3
2
2
3
2
2
=2x3
2)
4) Work out the following for the word:
PROBABILITY
2
6
4
7
(a) P(B) = 11 (b)P(Vowel) = 11
(c)P(Consonant) = 11
143°
143°
Corresponding angles
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EXAMPLES
1) A dentist keeps a record of the number of fillings she gives her patients over 2 weeks. Here are
her results:
Total =150
Estimate the probability that a patient does not need a filling
80
150
=
8
15
2) A company manufactures items for computers. The number of faulty items is recorded as shown
below:
(a) Copy and complete the table
8
100 = 0.08
20
200 = 0.1
45
500 = 0.09
82
1000 = 0.082
(b) Which is the best estimate of the
probability of an item being faulty?
Explain your answer.
The more trials you carry out the
more accurate your result
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TASK (LEVEL 6)
1)Flip a coin 100 times and record the results in the frequency table below:
Work out the following:
(a) P(Heads) =
(b) P(Tails) =
(c) How does the experimental probability
compare with the theoretical probability?
(d) Do you think the coin is fair or biased? Explain
(e) How can we increase the accuracy of our experimental probability?
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TASK (LEVEL 6)
2)Marie made a five-sided spinner, like the one shown in the diagram. She
used it to play a board game with her friend Sarah.
The girls thought that the spinner was not very fair as it seemed to land on
some numbers more than others. They threw the spinner 200 times and
recorded the results.
TOTAL
= 200
(a) Work out the experimental probability of each number.
19
27
32
P(1) = 200 P(2) = 200 P(3) = 200 =
4
25
53
69
P(4) = 200 P(5) = 200
(b) How many times would you expect each number to occur if the spinner
1
of 200 = 40
is fair?
5
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EXTENSION (LEVEL 6)
1) Naseer throws a fair, six-sided dice and records the number of sixes that
he gets after various numbers of throws. The table shows his results.
2
10
=
1
5
4
50
=
2 10
1
=
25 100
10
21
200
74
37
=
500 250
163
1000
329
2000
(a) Calculate the experimental probability of scoring a 6 at each stage that
Naseer recorded his results.
(b) How many ways can a dice land? 6
1
(c) How many of these ways give a 6? 6
1
(d) What is the theoretical probability of throwing a 6 with a dice? 6
(e) If Naseer threw the dice a total of 6000 times, how many sixes would
you expect him to get? x
1
of 6000 = 1000
6
÷
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THE CHECKOUT GAME RULES
1) This is a two-player game. Each player receives 12 tokens representing
music CDs.
2) Each player places the tokens in any of the checkout aisles marked 1-12 in
the store on his/her side of the board. Choose any of the aisles you desire,
putting any number of tokens on a space as you would like.
3) Take turns rolling two dice. On each roll, determine the sum of the dice. If
you have CDs in that numbered checkout aisle, move one CD to the parking
lot.
4) The winner is determined by the first player to have all of their CDs in the
parking lot.
TASK
What is the best arrangement for the CDs?
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PLAYER 2
11 12
11 12
Sound Store
8
7
6
5
4
3
2
1
Parking Lot
9 10
9 10
8
7
6
5
4
3
2
Music Mart
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THE CHECKOUT GAME
PLAYER 1
1
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POSSIBILITY SPACE FOR CHECKOUT GAME
DICE 1
DICE 2
+
1
2
3
4
5
6
1
2
3
4
5
6
7
2
3
4
5
6
7
8
3
4
5
6
7
8
9
4
5
6
7
8
9
10
5
6
7
8
9
10
11
6
7
8
9
10
11
12
36 Outcomes
(numbers in black)
Work out the probability for each checkout aisle number
1
36
2
P(3) = 36
3
P(4) = 36
5
P(6) = 36
6
P(7) = 36
5
36
4
1
P(9) = 36 = 9
3
1
P(10) = 36 = 12
2
1
P(11) = 36 = 18
1
P(12) = 36
P(8) =
P(2) =
1
= 18
1
= 12
=
1
6
1
2
12
1
P(Multiple of 3) = 36 = 3
18
1
P(Odd sum) = 36 = 2
30
5
P(Sum ≥ 5) = 36 = 6
15
5
P(Sum < 7) = 36 = 12
P(Even) =
18
36
=
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THE HOG DICE GAME RULES
1) Players take turns rolling fair six-sided dice. Any number of dice can be used but
it is recommended that at least ten dice are available for each player or team.
2) Players may choose how many dice they roll from turn to turn. The number of
dice rolled will be between one and the maximum amount available.
3) If any one of the dice rolled turns up a one, the player’s score is zero. If a one is
not rolled, then the score is the sum of the dice.
4) If a player rolls a one, the score is zero for that turn only; it does not set the
cumulative score to zero.
5) Players or teams keep track of their scores. A cumulative running score is kept.
6) A player or team to reach or exceed a predetermined score is the winner. Using
100 as the predetermined is one idea. If on the same turn more than one player
reaches the predetermined score, than the player with the higher total is the winner.
TASK
What is the optimal number of dice to roll to get the highest score?
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THE HOG DICE GAME DATA RECORD EXAMPLE
+
+
+
+
+
+
+
+
+
+
+
+
+
+
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THE HOG DICE GAME DATA RECORD SHEET
(TEACHER V STUDENTS)
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THE HOG DICE GAME
Expected scores, given no ones, for rolling 1-10 fair six-sided dice.
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THE HOG DICE GAME
Expected scores, given no ones, for rolling 1-10 fair eight-sided dice.
The best strategy on an eight-sided dice would be to roll either seven or
eight dice.
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THE HOG DICE GAME
Expected scores, given no ones, for rolling 1-10 fair ten-sided dice.
The best strategy on an ten-sided dice would be to roll either nine or ten dice.
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DISCOVERY
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LINK BACK TO OBJECTIVES
- Accurately calculate the experimental
probability of events occurring.
What level
are we
working at?
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PLENARY ACTIVITY (AFL CARDS)
A drawing pin is repeatedly dropped in an
experiment to see which way up it will land.
Here are the results:
Outcome
Point up
Point down
Frequency
15
5
What is the probability that it will land
point up?
b:
3
4
c:
5
20
Team
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a:
10
20
d:
3
4
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PLENARY ACTIVITY (AFL CARDS)
A coin is repeatedly thrown 60 times in
an experiment to see which way up it will
land.
Here are the results of the experiment:
Outcome
Heads
Tails
Frequency
27
33
What is the probability that it will land
head up?
b:
10
20
c:
35
50
Team
Worker
a:
33
60
d: 27
60
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PLENARY ACTIVITY (AFL CARDS)
Here are the results of a survey of cars passing a
school:
Colour
Red
Black
Silver
Other
b:
25
30
Number of What is the probability of the next
car passing the school being
cars
silver? (Simplify answer)
3
10
15
a: 15
2
10
c:
1
2
d:
3
30
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PLENARY ACTIVITY (AFL CARDS)
Here are the results of a survey of cars passing a
school:
What is the probability of the
Colour Number of
next car passing the
cars
school being black?
(Simplify answer)
Red
3
Black
10
Silver
15
a: 1
Other
2
10
b:
2
30
c:
1
3
d: 10
30
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PLENARY ACTIVITY (AFL CARDS)
Molly asked number of people about their age and
recorded it in a table.
Age
Group
0 - 20
21 – 40
41 – 60
60 +
b:
41
80
Number of
People
15
24
18
23
c:
39
80
Team
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What is the experimental
probability that the next
person Molly ask’s is aged
over 40?
a: 15
80
d: 23
80
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PLENARY ACTIVITY (AFL CARDS)
An ice cream shop recorded the number of customers
purchasing ice creams of each of the four flavours available.
Flavour
Vanilla
Chocolate
Strawberry
Peach
b:
12
50
Number of
Customers
12
18
9
11
c:
20
50
What is the experimental
probability that the next
customer will purchase a
Vanilla or chocolate ice
cream?
a:
30
50
d: 38
50
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PLENARY ACTIVITY (AFL CARDS)
Here are the results of a survey of cars passing a
school:
What is the probability of the
Colour Number of
next car passing the
cars
school being Red or other?
(Simplify answer)
Red
3
Black
10
Silver
15
a: 1
Other
2
10
b:
5
30
c:
1
3
d:
1
6
What have you learnt?
Draw your brain
In your brain, write or draw everything you can remember about
calculating the experimental probability of events occurring. 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 level
are we
working at?
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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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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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