Transcript probability-stats

PROBABILITY in
the new
curriculum
AMA Statistics Day
1 September 2007
Louise Addison
[email protected]
http://events.stanford.edu/events/86/8619/
A thought
provoker
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What topic is this from?
Where have I seen it before?
What does it mean?
What would a question look like?
Is it Achieve / Merit / Excellence level?
Could I draw a picture of it?
What connections can I make?
Do I need to find out more?
A Thought
Provoker
What do you think…
P(X) = 0
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Algebra?!
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Probability of Event X
is 0
Pig Flying…
Event X is impossible
P(X’) = 1
If X = A  B then A
and B are mutually
exclusive
0 is the probability of
Lotto rounded to 6
d.p.
A couple of ads…
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Link
NCEA Level One
 Put
these topics in order from best
done to worst done in Level One in
2006:
Algebra
 Geometry
 Graphs

Number
 Probability
 Trigonometry
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NCEA Level 1 2006
Not
Achieved
Achieved
Merit
Excellence
Number
16
50
24
10
Trigonometry
26
47
22
5
Geometry
32
48
16
4
Algebra
37
34
18
10
Graphs
38
46
14
1
Probability
45
31
20
4
Why?
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Sort the probability misconceptions
cards into groups…
TRUE OR FALSE?
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I’ve spun an unbiased coin 3 times
and got 3 tails. It is more likely to
be heads than tails if I spin it again.
TRUE OR FALSE?
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Waikato plays netball against
Auckland and can win, draw or lose.
Therefore the probability Auckland
will win is 1/3.
TRUE OR FALSE?
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There are 3 red beads and 5 blue
beads in a box. I pick a bead at
random. The probability that it is
red is 3/5.
TRUE OR FALSE?
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I roll two dice and add the results.
The probability of getting a total of
6 is 1/12 because there are 12
different possibilities and 6 is one of
them.
TRUE OR FALSE?
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A
There are more black balls in box A than in box
B. If you choose 1 ball from each box you are
more likely to choose a black ball from A than
from B.
B
TRUE OR FALSE?
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Tomorrow it will either rain or not
rain, so the probability that it will
rain is 0.5.
TRUE OR FALSE?
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Mr Brown is to have an operation.
90% of the people who have this
operation make a complete
recovery. There is a 90% chance
that Mr Brown will make a complete
recovery if he has this operation.
TRUE OR FALSE?
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If six fair dice are thrown at the same
time, I am less likely to get
1,1,1,1,1,1 than 1,2,3,4,5,6.
TRUE OR FALSE?
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It is harder to throw a six than a
three with a die.
TRUE OR FALSE?
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Each spinner has two sections, one
black and one white. The
probability of getting black is 50%
for each spinner
TRUE OR FALSE?
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I flip two coins. The probability of
getting heads and tails is 1/3
because I can get Head and Heads,
Heads and Tails or Tails and Tails.
TRUE OR FALSE?
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John buys 2 raffle tickets. If he
chooses two tickets from different
places in the book he is more likely
to win than if he chooses the first
two tickets.
TRUE OR FALSE?
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13 is an unlucky number so you are
less likely to win a raffle with ticket
number 13 than with a different
number.
13
TRUE OR FALSE?
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It is not worth buying a lotto ticket
with 1, 2, 3, 4, 5, 6 on it as this is
less likely to occur than other
combinations.
TRUE OR FALSE?
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My granddad smoked 20 cigarettes
a day for 60 years and lived to be
90, so smoking can’t be bad for
you.
TRUE OR FALSE?
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I have thrown an unbiased dice 12
times and not yet got a 6. The
probability of getting a six on my
next throw is more than 1/6.
Misconceptions about
probability
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All events are equally likely. 
Some events are less / more
likely than others
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(Representative Bias 123456)
Later events may be
affected by or compensate 
for earlier ones.
(Recency Bias - BBBBBG)
When determining
probability from statistical
data, sample size is
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irrelevant.
Results of games of skill are
unaffected by the nature of
the participants.
Lucky/Unlucky numbers, etc.
can influence random events.
In random events involving
selection, results are
dependent on numbers rather
than ratios.
If events are random then the
results of a series of
independent events are
equally likely, e.g. Heads
Heads (HH) is as likely as
Heads Tails (HT).
When considering spinners,
probability is determined by
number of sections rather
than size of angles.
Curriculum key
ideas
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Investigating situations involving chance (L1-5)
Exploring possible outcomes (L1-3)
Acknowledging uncertainty (L2-3)
Comparing experimental results with
expectations (L3-4), with theoretical results (L5)
Acknowledging variation (L3-5)
Acknowledging independence (L4-5)
Using fractions and percentages (L4-5) and
ratios (L5)
Comparing population parameters with those of
sample (L6)
Meteor Madness
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Investigating situations involving chance
(L1 - 5)
Exploring possible outcomes (L1-3)
Acknowledging uncertainty (L2 - 3)
Comparing experimental results with
expectations (L3-4), with theoretical
results (L5).
Acknowledging variation (L3 - 5)
Acknowledging independence (L4 - 5)
Using fractions and percentages (L4-5)
and ratios (L5)
Comparing population parameters with
those of sample (L6)
Rock / Paper /
Scissors
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Investigating situations involving chance
(L1 - 5)
Exploring possible outcomes (L1-3)
Acknowledging uncertainty (L2 - 3)
Comparing experimental results with
expectations (L3-4), with theoretical
results (L5).
Acknowledging variation (L3 - 5)
Acknowledging independence (L4 - 5)
Using fractions and percentages (L4-5)
and ratios (L5)
Comparing population parameters with
those of sample (L6)
The truth of the
matter
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Investigating situations involving chance
(L1 - 5)
Exploring possible outcomes (L1-3)
Acknowledging uncertainty (L2 - 3)
Comparing experimental results with
expectations (L3-4), with theoretical
results (L5).
Acknowledging variation (L3 - 5)
Acknowledging independence (L4 - 5)
Using fractions and percentages (L4-5)
and ratios (L5)
Comparing population parameters with
those of sample (L6)
Two way tables
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Power point teaching tool
Rocket launch
simulation
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Spreadsheet
A couple of
contexts
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Rock Paper Scissors
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Murphy’s Law
Correlation /
causation
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Power point
Discuss…
context
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I graduated from Douglass College
without distinction. I was in the top 98%
of my class and damn glad to be there. I
slept in the library and daydreamed my
way through history lecture. I failed math
twice, never fully grasping probability
theory. I mean, first off, who cares if you
pick a black ball or a white ball out of the
bag? And second, if you're bent over
about the color, don't leave it to chance.
Look in the damn bag and pick the color
you want.
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Plum, Stephanie
Hard Eight
Theoretical vs
experimental
probability
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"In theory, there is no difference
between theory and practice. But, in
practice, there is."
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- Jan L.A. van de Snepscheut
A concluding
thought…
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Always be a little improbable.
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Oscar Wilde