Transcript File

WHAT WOULD YOU DO WITH A MILLION
DOLLARS?
Invest in the
fishing industry!
HOW MIGHT YOU FIND YOURSELF WITH THIS
AMOUNT OF MONEY?
These people won 2.4
million pounds……..
https://www.youtube.com/watch?v=zHRNEcqCH
dg&list=PL42E007F2014C7B7D
This man won $168 million
https://www.youtube.com/watch?v=_C1gijCuTlI&
list=PL435B69FA5078E4D3
Question
Do these people live ‘happily ever after’ as
millionaires?
See what this man has to say…
https://www.youtube.com/watch?v=GWI2IgEYW
UI&index=13&list=PL42E007F2014C7B7D
WHAT ARE THE
CHANCES?
Understanding the odds of winning the lottery:
https://www.youtube.com/watch?v=_C1gijCuTlI&
list=PL435B69FA5078E4D3
Questions
Knowing the odds can be useful in winning
games such as lottto – are there other games
that involve chance?
One form of lotto requires choosing 6 numbers
out of 49 – do you think there is a good chance
of winning?
The chances of winning are: 1 in 13,983,816
REALITY CHECK
Statistics professor Stephen Clarke, from
Swinburne University, calculated the odds of
hitting the big one back in 2006.
"The average Australian, even if they buy their
ticket a couple of hours before the draw is made,
they've got more chance of dying before the
draw is made than they have of actually winning
the first prize," Dr Clarke says.
WHO WANTS TO MAKE
HISTORY?
80,658,175,170,943,878,571,660,636,856,403,766,975,28
9,505, 440,883,277,824,000,000,000,000.
To give you an idea of how many that is, here is how long it
would take to go through every possible permutation of cards. If
every star in our galaxy had a trillion planets, each with a trillion
people living on them, and each of these people has a trillion
packs of cards and somehow they manage to make unique
shuffles 1,000 times per second, and they'd been doing that
since the Big Bang, they'd only just now be starting to repeat
shuffles.
STATEMENT OF INQUIRY
Logic and modeling can change our justifications
for decision-making.
Question:
How can knowing about probabilities help us in
different areas of our lives?
THE STOCK MARKET
GUIDING QUESTIONS
How can people use information about the likelihood of events to
guide their decisions?
How effective is it to use probability and modelling to help us to
make judgments about future events?
THE BASICS:
How is the probability of success or failure for a particular situation
calculated?
The following activity will help us discover this:
Activity
Materials per group:
One pack of 52 cards (remove jokers)
Two A3 pieces of paper
Marker pens
Instructions
1) Sort the cards into suits:
Hearts
Diamonds
Clubs
Spades
How many cards are there in each suit?
Instructions
Sort each suit in the following order:
Ace, two, three, four, five, six, seven, eight, nine, ten, jack, queen, king
Questions:
1) How many cards are there in each suit?
1) How many ‘face cards’ (jack, queen, king) are there in each suit?
1) How many twos are there in a pack of cards?
Probability with cards
Instructions:
Problem 1: Put all the spades to the left side of your piece of paper.
Put all the red cards to the right of your piece of paper.
Use this to do a Venn Diagram on the paper showing the events of
S = drawing a spade and
R = drawing a red card
(include the number of cards for each event inside each circle)
Venn diagram
E = 52
In your groups work out and
write down on your paper:
13 (Clubs)
S
R
13
Pr(a spade) =
26
Pr (a red card) =
Pr (a spade or a red card) =
Pr (a spade and a red card) =
Another question
Instructions:
Problem 2: Put all the spades to the left side of your second piece of
paper.
Put all the face cards to the right of your piece of paper.
Is there a problem?
Now do a Venn Diagram on the second paper showing the events of
S = drawing a spade and
F = drawing a face card
E = 52
In your groups work out and write
down on your paper:
S
F
Pr(a spade) =
Pr (a face card) =
10
Pr (a spade and a face card) =
Pr (a spade or a face card) =
30
3
9
Probability Review
Ex 1.1 of textbook
What are Mutually
Exclusive Events?
If two events cannot occur at the same time they
are called mutually exclusive events.
Addition Law for Mutually Exclusive Events:
If A and B are mutually exclusive events then:
Pr(A or B) = Pr(A) + Pr(B)
Mutually Exclusive Events
How do we know that events
A and B are mutually
exclusive?
Because there is
no overlap.
Mutually Exclusive Events
P(A or B) = P(A) + P(B)
or
P(A ∪ B) = P(A) + P(B)
Are these events mutually exclusive?
Another situation
Here is a Venn diagram
showing the numbers of
students who do archery
event (A) and badminton
(event B):
E = 100
A
B
22
Question: if we know that a
particular student does
badminton, how does this
affect the probability that they
also do archery?
16
14
E = 100
How many play
badminton?
30
How many of these also
do archery?
16
So what we need to work
out is the probability that
a student does archery,
given that they do
badminton.
A
B
22
Pr( student does
archery given they
play badminton)
16
14
= n(archery ∩ badminton)
n(badminton)
= 16
30
This is called conditional probability because there is a
condition on the outcome of event A – ie it depends on the
condition imposed by outcome B
Conditional Probability
In probability terminology:
Pr(A\B) = Pr(A ∩ B)
Pr(B)
16
= 100
30
100
= 16
30
=8
15
Conditional probability with tree diagrams
A company has two factories where it manufactures sports shoes. It is known that 65% of the
shoes are made at factory A . It is also known that 10% of the shoes made at factory A are
faulty, but the fault rate at factory B is only 7%.
a) Draw a tree diagram
for this information.
0.1
0.65
F
A
0.9
0.07
0.35
First we need to find the sample space
– all faulty shoes:
Pr (AF) = 0.65 x 0.1 = 0.065
F’
F
B
0.93
b) If a pair of shoes is randomly
selected from the company’s stocks,
find the Pr (the shoes are from factory
A, given that they are faulty)
F’
Pr (BF) = 0.35 x 0.07 = 0.0245
So Pr(F) = 0.065 + 0.0245 = 0.0895
Now find Pr(A∩F)
Pr(A\F) = Pr(A∩F)
Pr(F)
= 0.065
= 0.065
0.0895
= 0.7263
There is a 73% chance that the faulty shoes will be from factory A
How useful is this maths?
Could this being useful to analyze real life situations?
Who in particular might find this information useful?
Discussion:
Is it reasonable to use probability information to
predict human behaviour?