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Probability assignment
November 4, 2008
You and some classmates need to create a game for a booth at the school carnival. The game should be easy to make and set up. I should be fun, too, but it mustn’t take long to play.
You can use spinners, dice, coins, cards or any other random selection device.
Your game does not have to be completely original, but the probability must be well explained.
Play your game 10 times. Record your results.
Do these results match your expectations?
Instructions: Explain the rules of your game.
Probability: Use Probability to express your expectations.
Present the results of actually playing the game 10 times.
Presentation: Show pride and creativity in your work.
Here is the Scoring Guide for this Assignment
100%-80% 80%- 60% 60%- 40% below 40%
|
Instructions |
Above Expectations |
At Expectations |
Some Effort |
No effort Below Expectations |
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Probability |
Probability is explained. Math is clear and correct Excellent |
Probability is partially explained.
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Probability is not explained in enough detail. |
No probability is involved or is poorly presented |
|
Presentation |
Game board or game is artistic and creative. |
Game board or game has had some effort in its creation. |
Game board was done at the last minute and shows little effort. |
Game board or game shows a lack of pride or effort. |
|
Bonus |
Above and beyond the call of duty. In all aspects of the game board, probability and clarity of instructions.
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Less than excellent. |
|
|
Samples
Queen of Hearts
The game
- It cost $1 to play.
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Using a regular deck of cards, select three cards at random.
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Turn over three hearts in a row and you win $10.
- If one of the three hearts is the Queen of hearts you win $20
Probability
P = P1 x P2 x P3
P= (13÷52) x (12÷51) x (11 ÷ 50)
P= 1716 ÷ 132,600
P = .0129
P= 1.3% change of winning
Out of 100 games the house will win one dollar 98.7 times or $98.7
The house would pay out $10 x 1.3 times or $13.
The expected profit per hundred games $100 – 13 = $87
The probability that one of the hearts is the Queen of hearts would occur.
P = P1 x P2 x P3
P= (13÷52) x (1÷51) x (11 ÷ 50)
P= 143 ÷ 132,600
P = .001078
Once per thousand
So once in 1,000 games there would be one $20 payout.
For 1,000 games we would expect a payout of 130 + 20 = 150
Therefore the income would be $1,000 – $150 = $850
Perfect shot
Double your money!
Using a regular 8 ½ x 11 inch sheet of paper place four circles with a 3 cm diameter near the center and corners of the sheet.
$1 gets you two dart throws
For each black spot you hit you win $1
Probability
8.5 x 11 = 93 square inches
For the area of each circle we calculate
A= Õ r 2
A = 3.1416 x 1.5 2
A = 3.1416 x 2.25
A = 7.0686
X 4 = 28.27 square inches
P= e/r
P= 28.27 ÷ 93 = .304
P = 30.4 %
We would expect 30.4 out of 100 shots to hit the Black targets.
For 100 plays there would be 200 shots
30.4% hits = 30.4 x 2 hits or $60.8 payout
The house would expect to make $39.2 per hundred plays.
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Statistics Assignment
October 28, 2008Statistics Assignment
¨ Find two statistics of any kind and explain what they mean in your own words.
¨ Find one graph of any kind and explain the information in the graph in your own words.
Create graphs
¨ Broken line graphs
Track the price of gas for at least 14 days and place the information on a Broken line graph.
One graph to drawn by hand
One graph done on excel
¨ Circle graphs
Find the results of the Federal election 2008.
Make a circle diagram of the number of seats each party won.
Make a second circle diagram of the percentage votes each party won.
Draw each graph by hand and show your calculations
Do each grap on excel
(Total of four graphs)
¨ Horizontal bar graph
Select five realistic jobs you could do within the next five years.
Create a horizontal bar graph of the annual income of each job
Indicate the job you intend to pursue
(this graph can be done by hand or by using excel)
¨ Vertical bar graph
Your choice of topic
Your choice of cons ruction
¨ Pictograph
Your choice of topic
Your choice of cons ruction
¨ Create a frequency distribution chart
It may be on any topic
You must collect the information yourself by asking questions or observation.
(We did an example in class about the age of the class)
¨ Create a data table
On any subject that is relative to your life.
Explain how the subject is relative to your life.
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Subscribing to a service Algebraic modeling
October 14, 2008The best phone plan
A friend had just e-mailed me about two phone plans he had to choose from.
One cost .07 cent per minutes
The other had a flat rate of .32 cents per call plus .03 cents per minute.
My buddy asked which was better.
The short answer is “it depends on how much you talk.”
The mathematical answer is a bit better.
The cost of the first plan can be expressed as
Cost = seven cents per minute
Let y= cost
Let x = number of minutes
Y= .07 x
The second equation can be expressed as
Cost = . 03 cents per minute plus .32 cents
Y = .03 x + .32
To find which is best find the point where they are the same cost.
.07 x = .03x + .32
Solve for x
.07 x – .03x = .32
.04 x = .32
x = 8
Therefore 8 minutes is the decision point
At 8 minutes the two costs are the same
.07 (8) = .56
and
.03 ( 8) + .32 =
.24 + .32 = .56
If the average phone call is less than 8 minutes then the first plan at .07 cents is best.
If the average phone call is more than 8 minutes then the second plan is better.
Draw the graph
$
Y = .07x
Y = .03 x + .32
Minutes
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Posted by robertmore
The value of a dollar
October 9, 2008The value of a dollar
One of the best measures of the value of a dollar is how long you have to work for something.
For example if you are working for $8 per hour and want to buy something that cost $80
You may say that the item is worth ten hours of work.
$80 ÷ 8 $/hr = 10 hrs
This is a good start to evaluating the value of goods.
However, this calculation assumes the income was not taxed, that you have no liabilities, and there is no tax calculated on the item you wish to purchase.
In reality the item cost more than 10 hours of work.
If you are taxed at 30% to 40% then you must earn more income before you have $80 in your hands.
There are costs to going to work such as transportation, lunches and special tools or clothing.
There are living expenses that must be covered before there is any money to buy toys or luxuries (Disposable Income)
Let’s take an example of working for $8 per hour.
$8 per hour 5 hours per day = $40 per pay
$40 x 5 = $200 per week.
From the $200 we will subtract 30% in deductions (and this is getting off easy)
200 x .30 = 60
So you have $140 for your 40 hour week (Net Pay)
If transportation is $2 per trip, or $4 per day then just getting to work costs $20 per week.
Subtract $20 from your $140 and you now have $120
If you spend about $4 on lunch and coffee each day then subtract another $20 for the week.
$120 –$ 20 = $100
So you have about $100 for your 40 hour week.
You have earned about $2.50 per hour in your hands.
This assumes you have no other liabilities.
Now for the item you wanted to buy. We said it had an $80 price tag.
The Goods and services tax 6% and the Provincial sales tax 7% add 13% to the cost of the item.
80 x 1.13 = 90.40
$90.40 ÷ 2.50 $/Hr = 36.16 hrs
Daddy buy me an $80 MP3 PLAYER
You may think that if your father is working at $25 per hour that he could buy the MP3 PLAYER for you in 3.2 hours.
($80 ÷ $25)
That sounds reasonable, but what are you going to do around the home to release your Dad for the time.
Let’s look at the numbers again, this time taking some of the other costs into consideration.
Dad earns $25 per hour and works 40 hours a week.
25 x 40 = $1000
But dad is taxed at 40%
$1000 x .40 = 400
$1000 – 400 = 600
Dad drives a car to work.
Gas alone is $30 per week
Other car expenses can easily be allocated to $100 per week
(Lease, depreciation, maintenance, insurance, registration, licence)
$600 – $130 = $470
Dad probably eats and has coffee at work. Say $5 per day
Subtract another $25
This leaves $445
However, dad has a few expenses that must be covered before spending anything on an MP3 PLAYER.
RRSP 50
Rent 200
Hydro 30
Phone 20
Food 100
And likely a few others
So subtract $400
$445 – $400 = $45
So at the end of the week there is a surplus of $45
The $45 is deposable income.
It can be spent on just about anything.
It took 40 hours to earn this $45
45 ÷ 40 = $1.125 per hour.
The $80 MP3 Player will cost 90.40 with taxes.
It represents $90.40 ÷ 1.125 = 80.35 hours of work.
Now what are you willing to do to make up for the effort Dad put in to buy an MP3 Player.
Is there anything else that would benefit the family more than and MP3 player?
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Purchasing or leasing a commodity, The cost of my car
September 30, 2008
The cost of my car.
Check each box as you complete the task.
q Select the car you intend to drive.
If you have a car you may use it as your sample.
If you do not have a car you must select one within your current economic means.
Calculate the following:
q Cost to buy this car
q Cost to buy this car second hand
q Cost to lease this car
q Calculate the cost of running the car you selected for car for one year.
Include as many details about the cost as possible.
The cost of fuel.
As the price of fuel increases it has an effect on the cost of running the car.
q Calculate the cost of filling the tank of your selected car.
q Find out how far your selected car can drive on one full tank of gas.
q Draw a graph using the two intercept points.
Use the cost for the Y access and Kilometres for the X access.
Calculate the slope; it will be the cost per kilometre for your car.
Cost of filling the car with gas.
(Tank capacity multiplied by the price of gas.)
Kilometres
(Number of km the car will drive on a full tank of gas.)
Administrative costs.
Aside from gas and oil you car has certain mandatory administration costs.
Calculate the annual costs for
q Registration
q Insurance
Tickets
It can happen if you make an error
Find out the following costs of a ticket in your area for the following
Bonus if you can find the point reductions.
q Parking ticket
q Stop sign violation
q Speeding
Student Sample of a completed assignment
Name _____________
Toyota Echo
Cost new $14,086
Plus financing costs
Cost used $8,000
Lease $230 per month
Annual cost $230 x 12 = $2,760
Over 5 years $2760 x 5 =13,800
Buy New
I would select the buy the new car because I would expect to have the car for more than 5 years.
I like the new car look and feel. I do not want to buy someone else’s problems
I could sell the car at any time.
A lease agreement places a number of restrictions on me.
Restricted number of kilometres.
Specified maintenance program.
Buy used
I would buy a used car
The car is to get me to work not a show piece.
A second hand car will not cost me as much in insurance.
I would not have to take out a bank loan to purchase the car.
I would not have to follow a prescribed maintenance program.
Lease
I would lease the car
I like to change the car I drive in three years.
I never want to have an old clunker that may break down on me.
I want a maintenance system that ensures the car will run properly.
The cost of gas
Calculate the slope, it will be the cost per kilometre for your car.
To fill the car with gas cost $64
The car can drive 425 km on a full tank of gas
Cost (0,$64)
(425 km, 0)
Kilometres
Slope $/km dollars per kilometre
y2-y1 0-64 64
x2- x1 425- 0 425 .15 dollars per km
My drive to work 26 km
52 km per day cost is $7.80 per day
$39 per week
$156 per month using 5 days per week.
Tickets
Parking $42 cost in Lachine, no points deducted
Speeding 136 km in a 100 km zone $186 and three points.
The fine and points vary with the speed
Stop sign $104 and three points.
Cost of the car $8000
Registration $224
Insurance $535
Gas $156 per week
Oil $30 per 8,000km
Tires
Wind shield wash $2 per month
Car wash $3 per month
Maintenance $200 per year
Annual costs of running the car
20,000 km
Car 8000/5 $1600
Registration $224
Insurance $535
Gas $1872
Oil $90
Tires
Wind shield wash $24
Car wash $36
Maintenance $200
Total $4,581
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The break-even calculation.
September 25, 2008Becoming self employed Page 195
The break-even calculation.
Think of any small business you could make that requires a machine.
_______________________________________________________
Find the cost of several of these machines.
(Fixed cost)
_______________________________________________________
_______________________________________________________
_______________________________________________________
Which machine would you choose?
How much will it cost?
_______________________________________________________
_______________________________________________________
Why choose this machine?
_______________________________________________________
_______________________________________________________
How much will it cost to produce this good or provide this service?
(Variable cost)
How much will you charge for this good or service?
Calculate the profit on each item sold or each service provided.
Price – Variable cost. = contribution margin
How many units would you have to produce to cover the cost of the machine?
Fixed cost / contribution margin
How many jobs could you do in one day?
How many days would it take to pay for the machine?
It this worth buying
Why?
Why not?
The break-even calculation. Example
Think of any small business you could make that requires a machine.
Snow clearing
Find the cost of several of these machines.
(Fixed cost)
Sears Craftsman $ ____________
Wal-mart $_____________
Canadian Tire $ ____________
Which machine would you choose?
How much will it cost?
Sears
$1,000
Why choose this machine?
According to the website information this one ranked the highest in dollars to value.
http://www.Consumer magazine
How much will it cost to produce this good or provide this service?
(Variable cost)
$5
How much will you charge for this good or service?
$25
Calculate the profit on each item sold or each service provided.
Price – Variable cost. = contribution margin
$25 -$5 = $20
How many units would you have to produce to cover the cost of the machine?
Fixed cost / contribution margin
1,000 / 20 = 50
This means that it would take 50 jobs to pay for the machine.
How many jobs could you do in one day?
5
How many days would it take to pay for the machine?
50 jobs / 5 jobs per day = 10 days
It this worth buying?
Why?
Yes, it would be great to have a good snow blower and make enough money to pay for it.
I could even start a little side business on
Why not?
I hate going outside in the winter.
I cannot transport a snow blower on the bus
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Posted by robertmore
Credit card debt Incurring debt
September 19, 2008Credit card debt
Having a credit card instantly increases the ability to purchase.
It is a tempting lure most cannot pass up.
The cost of using credit is interest.
If you can understand the cost of credit you are less likely to become a statistic of credit card indebtedness.
Consider this.
Very few rich people pay credit card interest.
Most personal bankruptcies involve credit card debts.
All financial advisers will begin with eliminating credit card debt.
Cost of credit.
Most cards will cost between 18% to 20% interest.
The interest is compounded based on the previous balance.
If you purchase an item for $500 and pay cash the item will cost $500.
If you purchase the same item on a credit card and make minimum payments then the same item will cost about $1000.
(Yes, double the price)
http://www.vertex42.com/Files/credit-card-payoff-calculator.xls
This is an excellent credit card calculator.
For this class we will do it the old fashion way with a pencil and paper.
$500 with a 2% interest rate per month paid by instalments of $50 per month.
500 – 50 = 450
450 * .02 = 9
459 -50 = 409
409* .02 = 8.18
417.18 – 50 = 367.18
367.18 * .02 = 7.34
Continue
Now save time and write the formula on exce
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Amount |
500 |
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Interest |
2% |
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Payment |
50 |
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Amount owed |
Balance |
Interest |
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500.00 |
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500.00 |
450.00 |
9 |
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459.00 |
409.00 |
$8.18 |
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417.18 |
367.18 |
$7.34 |
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374.52 |
324.52 |
$6.49 |
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331.01 |
281.01 |
$5.62 |
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286.63 |
236.63 |
$4.73 |
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241.37 |
191.37 |
$3.83 |
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195.19 |
145.19 |
$2.90 |
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148.10 |
98.10 |
$1.96 |
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100.06 |
50.06 |
$1.00 |
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51.06 |
1.06 |
$0.02 |
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1.08 |
-48.92 |
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Calculating the 15% TIP at a restaurant (P 196)
September 18, 2008Calculating the 15% TIP at a restaurant
Far too often the calculation of a tip causes an uncomfortable moment at the end of a meal.
There are several ways to make the calculation easy and painless.
- The tip is about equivalent to the combined GST and PST in Quebec.
- Multiply the total by .15
- *Multiply the cost of the meal by 10% and then add half.
Let me explain this third option.
A stress free way to calculate the TIP is to calculate 10% of the Meal cost.
Then add half of that result to the total.
For example a $60 meal calculate the 15% TIP
60 x .10 = 6 (10%)
6 ÷ 2 = 3 (5%)
9 (15%)
A 15% TIP will be $9
This is the same result as multiplying by .15
60
x .15
300
600
$9.00
Try other amounts
$56 = $8.40
$30 = $4.50
In a very short time the calculation will become simple.
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Understanding the TSX composite index
September 16, 2008Understanding the TSX composite index
The Toronto Stock Exchange, TSX main index was at 13,000 in the beginning of September 2008.
The number is in every newspaper and it is a regular part of every newscast on television.
Very few people know what the number is.
There has been a drop of 500 points in the past few days.
“The market is in a tailspin.”
1. What does the 13,000 mean?
2. What does a drop of 500 points mean?
Let me answer the first Question.
What does a composite index of 13,000 mean?
In 1977 the Toronto Stock Exchange took a group of 300 influential Canadian stocks.
The value of the stocks was calculated and given a base value of 1000.
In 2008 the composite index was 13,000
In theory a $1 investment in 1977 would be worth $13 in 2008.
NOTE
The stocks and the weighting of the stock in the index change over time.
The 1:13 ratio is not perfect, but it is a good indicator.
To answer the second question.
What does a drop of 500 points mean?
100 points = 1%
A drop of 500 points would be a drop of 5%
If you have $1,000 invested in Canadian stocks and the market is down 500 points how much would your investments be worth today?
1000 x -.05 = -50
On average you would have lost $50.
Your investments are now worth $950
NOTE
Unless you have invested in the exact mix of stocks used in the TSX composite index, the value of your portfolio will not be reduced by exactly $50, however the index remains a good indicator of the markets.
Should we panic?
I cannot think of an instance when panic is the best option.
Consider the factors
How much do you have invested in the market?
How much do you rely on the income from the market?
Which companies’ products are directly affected by the change in the market?
What there spin-off affects of the market change?
Has the market change created new opportunities?
If you are a student with no investments there is little in this market fluctuation that will affect you directly.
If you have been working for Merle Lynch for many years, facing job loss, a huge mortgage and now rely on your investments to finance a retirement. Your view of this market correction is a little more desperate.
One analyst made reference that it has been one of the darkest days ever.
Certainly the market analyst has a substantial amount of assets in the market and for his household it may be one of the darkest days.
I would argue that it is not darker than:
The total crash of 1929
The days when Germany might have won the war.
When the Cuban missile crisis threatened to plunge us into nuclear war.
Or even when the war on terror was sparked by the attack on 9:11
Understand what the change means to you and put the change into prospective.
Market correction
A market correction is a sudden decrease in the price of stocks. It could be a 10% – to 20% drop.
The term Correction has a positive connotation, something that should happen.
If you have a substantial amount of money invested in the market a “market correction” may not seem like a very good thing.
So what is a market correction?
The value of a company can be calculated.
Take the value of the stock and multiply by the number of stocks
10,000 stocks at a price of $5 make for a company worth $50,000
Conversely if you take a $100,000 company with 100,000 stocks the value of each stock should be $1.
As the company increases in value and assets to $200,000 we would expect the value of the stock to increase to $2 per share.
This can be the beginning of the problem.
Speculators see a price go from $1 to $2
This is a good stock so people buy it.
The demand for the stock increases the price, and then the sock price increases to $3.
The increase in price may spark more speculation. Demand pull increases the price to $5.
The real value of the company has not changed from $200,000.
The real value of the stock is $2
Once a group of investors begin selling their stock to take profits the value of the stock drops.
As the stock price drops more people may dump the stock pushing prices back down.
The stock should drop to the price of $2.
$2 would be the “correct” value of the stock.
A huge panic sell of may push the price below $2, creating market opportunities.
How can you avoid becoming a victim of a market correction?
Know what you are buying.
Do not buy stock based on past performance.
Know something about the stock you are investing in.
Learn a little bit about the company you are investing in.
Most people have stocks do not even know where there money has been invested.
Peter Lynch once said
If you cannot explain to a ten year old why you have invested in a stock you should not be investing in it.
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