Date 1 Probability - Algonquin Achievement Centrejoansavoie.weebly.com/.../chapter_1_-_probability.pdf · 2020-02-01 · Date 978-0-07-090894-9 Chapter 1 Probability • MHR Chapter

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978-0-07-090894-9 Chapter1Probability•MHR�

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1 Probability

•Contests,lotteries,andgamesofferthechancetowinjustaboutanything.Youcanwinacupofcoffee.Evenbetter,youcanwincars,houses,vacations,ormillionsofdollars.

•Gamesofchancearedesignedsothatthecustomerlosesmostofthetime.

•Forexample,thechanceofwinningalotterywhereyoupick6numbersoutof49is1inalmost14million!Youhaveabetterchanceofbeingstruckbylightning.

1. a) Listcontests,lotteries,orgamesthatyouhaveentered.

_____________________________________________________

_____________________________________________________

_____________________________________________________

_____________________________________________________

b) Howoftenhaveyouwon?

_____________________________________________________

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Skills Practice 1: Fractions, Decimals, and Percents

1. a) You have several quarters. Write the amount shown in 2 ways.

Use a cents symbol ______ Use a dollar sign ______

b) Write the amount as a fraction of a dollar. Show the fraction in 2 ways.

______ = ______

c) Percent means “out of ______.” The amount shown in

part b) is ____% of a dollar.

2. This measuring tape shows 1 foot.

31 2 4 5 6 7 8 9 10 11 12

a) One foot equals ______ inches.

b) Half a foot is ______ inches.

c) How many inches are in 1 _ � foot? ____________

d) How many inches are in 3 _ � foot? ____________

e) Show 6 inches as a percent of 1 foot. ____________

f) Express 1 inch as a fraction of 1 foot. ____________

Another way of saying

one-fourth is one- .

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3. Withoutusingacalculator,completethetable.

Fraction Decimal Percent

1_2

1_4

3_4

0.2

0.3

80%

8�%

1_3

2_3

0.01

0.0�

8%

13%

0_10

10_10

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1.1 What’s the Chance? Focus: theoretical probability, number sense

Warm Up

1. a) How many weeks are in

1 year? ______

b) How many weeks are in half

a year? ______

2. a) How many seasons are in

1 year? ______

b) Each season is the same length. How many weeks

are in each season? ______

3. Add.

a) 0.1 + 0.2 + 0.3 + 0.4

= ______

b) 20% + 25% + 30% + 15%

= ______

c) 20 _ 100

+ 13 _ 100

+ 27 _ 100

+ 40 _ 100

= ______

4. What fraction of a dollar is each coin?

=

=

=

heart diamond club spade

Calculating Theoretical Probability

1. There are 52 cards in a standard deck of cards.• There are 4 different suits.• Two suits have red symbols. These are the hearts and

diamonds.• Two suits have black symbols. These are the clubs and

spades.• Each suit has numbered cards from 2 to 10, plus a jack,

a queen, a king, and an ace.

A

A

A

A

A

A

A

A

You have a full deck of cards. What is the probability of picking the following card?

a) a heart ______ b) a black card ______

c) a red card ______ d) an ace ______

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Pro

bab

ilit

y

Suit

100%

75%

50%

25%

0%

•Thechanceofsomethinghappeningisitstheoreticalprobability.

2. Useyouranswersfrom#1toshowtheprobabilityofpickingthefollowingcards.Showeachprobability3ways.

Write as a Fraction

Write as a Decimal

Write as a Percent

a) A Heart

b) A Black Card

c) A Red Card

d) An Ace

Gotopages1–2towritethedefinitionfortheoretical probabilityinyourownwords.

Gotopages1–2towritethedefinitionfortheoretical probabilityinyourownwords.

3. a) Whatistheprobabilityofpickingaclubfromafull

deckofcards?Writeyouranswerasapercent.______

b) Whatistheprobabilityofpickingadiamond?

Writeyouranswerasapercent.______

c) Createabargraphshowingtheprobabilityofpickingany1suitifyoupullonly1cardfromafulldeck.•Includeatitleforthegraph.

d)Whatistheprobabilityofpickingaclub,aspade,aheart,oradiamondfromafulldeck?Writeyouranswerasapercent.

_______________________________

_______________________________

e) Explainyouranswertopartd).

______________________________________________

______________________________________________

______________________________________________

______________________________________________

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4. a) What does this roll of a die show? ______

b) What is the probability of rolling a 2 with 1 die?

Write your answer as a fraction. ______

c) What is the probability of rolling a 5? ______

d) Create a bar graph showing the probability of rolling each number when you roll 1 die.• Include a title for the graph.• Label each axis.

e) What is the probability of rolling a die and getting

a 7? ______

f) Explain your answer to part e).

______________________________________________

5. You flip a coin. Create and label a circle graph showing the probability of getting heads or tails.• Include a title.• Label each sector.

Die is the singularform of the word

.

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6. a) Statetheprobabilityofthespinnerbelowlandingoneachcolour.Writeyouranswerasapercent.

yellow blue

blue

blue

blue

red

red

green

green green

Blue:________

Green:________

Red:________

Yellow:________

b) Whatistheprobabilityofthespinnerlanding

onyelloworblue?____________________________

c) Whatistheprobabilityofthespinnerlanding

ongreenorblue?____________________________

d) Whatistheprobabilityofthespinnernotlanding

onblue?___________________________________

✓Check Your Understanding

1. Fillineachblankwiththeappropriatephrase.

�It�will�happen.�It�is�not�likely�to�happen.��It�is�likely�to�happen.�It�will�not�happen.��It�might�happen,�it�might�not.

100%

51%–99%

50%

1%–49%

0%

_____________________________________

_____________________________________

_____________________________________

_____________________________________

_____________________________________

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1.2 In a Perfect World Focus: theoretical probability, experimental probability, number sense

Warm Up

1. Write 10 _ 40

in lowest terms.

10 _ 40

=

2. Write 3 equivalent fractions

for 1 _ 2 .

1 _ 2 =

3. Write 90% as a fraction in lowest terms.

4. What percent of the bar is shaded?

5. Shade 75% of the cylinder. 6. What is the chance of picking a king from a deck of 52 cards? Show your answer as a fraction in lowest terms.

Collecting Data to Calculate Probability

Imagine flipping this penny 10 times. In a perfect world you would get 5 heads and 5 tails. This is theoretical probability.

1. Answer the following questions as though you were in a perfect world.

a) What would happen if you flipped a coin 50 times?

______________________________________________

b) If you rolled a die 60 times, how many 3s would you

get? _____

c) If you cut a deck of cards 40 times, how many hearts

would you get? ________

2. In a perfect world, the ____________________

____________________ of flipping heads is 50%.

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• Experimental probabilityisthechanceofsomethinghappeningbasedonexperimentalresults.

•Aftercollectingdata,itisusefultocompareexperimentalprobabilitywiththeoreticalprobability.

3. a) Createandlabelabargraphshowingthe“perfectworld”resultsforrollingadie60times.•Titlethegraph.

b) Rolladieexactly60times.Recordyourresultsinthetallychart.

c) Createandlabelabargraphshowingyourresultsinpartb).

d) Foreachofyourresults,expresstheexperimentalprobabilityasafraction.

1=_____ 2=_____ 3=_____

4=_____ 5=_____ 6=_____

Gotopages1–2towritethedefinitionforexperimental probability inyourownwords.

Gotopages1–2towritethedefinitionforexperimental probability inyourownwords.

1

2

3

4

5

6

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4. a) Create and label a bar graph showing the “perfect world” results for cutting a deck of cards 40 times.• Title the graph.• Label each axis.

b) Record the results for obtaining each of the 4 suits when you cut a deck of cards exactly 40 times.

c) Create and label a bar graph showing your results in part b).

d) For each of your results, express the experimental probability as a fraction and then a percent.

Clubs: __________ or __________ %

Spades: __________ or __________ %

Hearts: __________ or __________ %

Diamonds: __________ or __________%

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5. a) Createandlabelacirclegraphshowingthe“perfectworld”resultsforflippingacoin50times.•Includeatitle.•Labeleachsector.

b) Flipacoinexactly50times.Recordyourresultsinthetallychart.

Heads Tails

c) Createandlabelacirclegraphfortheresultsobtainedinpartb).

✓Check Your Understanding1. a) Didanyoneintheclassget“perfectworld”results

forall3oftheexperiments?YES____NO____

b) Explainwhyfew,ifany,peopleintheclassreceived“perfectworld”resultsforall3oftheexperiments.

___________________________________________

___________________________________________

___________________________________________

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Tech Tip: Experimenting with a Random Number Generator

You can use a graphing calculator to simulate experimental probability.

Follow the instructions to check out several different applications.

Using a TI-83+ Graphing Calculator

1. Press MATH. Scroll right so that PRB is highlighted.

2. Press 5 to select 5:randInt(.This command tells the calculator to generate random integers.

3. a) To simulate flipping coins, enter 1,2).Make sure there are no spaces between the characters.

This tells the calculator to select either the number 1 or the number 2.Mentally assign heads or tails to each number. For example, 1 is heads, 2 is tails.Continue pressing the ENTER key to generate more random tosses.

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b) To simulate selecting the suit of a card, enter 1,4).Make sure there are no spaces between the characters.

A

A

A

A

A

A

A

A

This tells the calculator to select an integer from 1 to 4.Mentally assign 1 suit to each of the 4 numbers.Continue pressing the ENTER key to generate more random suits.

c) To simulate selecting the value of a card, enter 1,___).

d) To simulate selecting the exact card, enter 1,___).

e) To simulate rolling 1 die, enter 1,___).

4. Press ENTER. A random integer from the acceptable range of values will be displayed. Continue pressing ENTER to generate more random numbers.

heart diamond club spade

978-0-07-090894-9 Tech Tip: Experimenting with a Random • MHR 15Number Generator

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Skills Practice 2: Equivalent FractionsThe word “equivalent” comes from 2 smaller words.“equi” = equal“valent” = value

Equivalent fractions are fractions that have the same value.The top number of a fraction is called the numerator.The bottom number of a fraction is called the denominator.

3 _ 4

ExampleLook at the 3 bars below. Write the fraction of each bar that is shaded.

5

5

5

In this example, the same amount of each bar is shaded. These

visuals show _______________ _____________.

_____ = _____ = _____

1. a) Write the fraction of each bar that is shaded.

5

5

b) What is an equivalent fraction for 2 _ 3 ?

numeratordenominator

Go to pages 1–2 to write the definition for equivalent fractions in your own words. Give an example.

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2. Writethefractionofeachcirclethatisshaded.

a)

=_____

b)

=_____

c)

=_____

3. a)Write4equivalentfractionsfor1_2.

b) Explainorshowhowyoudevelopedthefourthfractionabove.

___________________________________________

___________________________________________

4. a)Develop3visualstoshowyourownequivalentfractions.

b) Writethefractions.

5. Fillintheblankstocreateequivalentfractions.

1_2=2_ = _

6=10_ =20_ = _

50= _

100=250_

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1.3 Roll the Bones Focus: theoretical probability, experimental probability, number sense

Warm Up

1. Write 3 equivalent fractions for 1 _

4 .

2. Write each fraction as a decimal.

1 _ 4 = 1 _

5 =

3. Write each fraction in lowest terms.

4 _ 12

= 6 _ 18

=

4. There are 15 students in a class. Five are girls. Write the fraction of the class that is girls in lowest terms.

5. The bar graph shows attendance at a movie theatre for 1 week.

a) How many people saw the movie on Wednesday?

________

b) How many people saw the movie on Friday?

________

c) How many people saw the movie last week?

________

Rolling Dice

1. Suppose you roll 2 dice.

a) What is the smallest total you can get? ______

b) What is the greatest total you can get? ______

c) How many different totals are possible? ______

d) If you roll a pair of dice 50 times, predict the number

of times that the total will be 7. ______

0

Sun

Mon Tues

Wed

Thur

s

Fri

Sat

50

100

150

200

250

300

350

Day of the Week

Movie AttendanceN

um

ber

of

Peo

ple

400

0

Sun

Mon Tues

Wed

Thur

s

Fri

Sat

50

100

150

200

250

300

350

Day of the Week

Movie AttendanceN

um

ber

of

Peo

ple

400

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2. a) Roll 2 dice exactly 50 times. Add the 2 numbers showing. Record the number of times each total occurs.

Sum of the Dice Tally

Total Times Rolled

2

3

4

5

6

7

8

9

10

11

12

b) Create a bar graph showing your results. • Include a title.• Title the y-axis, Total.• Title the x-axis, Sum

of the Dice.• Choose an appropriate

scale for the y-axis.

c) Did you roll each of the sums an equal number

of times? YES ____ NO ____

d) Suggest some reasons for your answer.

______________________________________________

______________________________________________

978-0-07-090894-9 1.3 Roll the Bones • MHR 19

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• There is only 1 way to roll a 2 with 2 dice. You need a 1 on each die.

• There are 2 ways to roll a 3. You can have a 1 on the first die and a 2 on the other. Or, you can have a 2 on the first die and a 1 on the other.

3. a) Determine all the possible combinations for rolling 2 dice. Example:

(1, 1)

Sum of the Dice Possible Combinations

Number of Combinations

2 (1, 1) 1

3 (1, 2) (____, ____) 2

4

5

6

7

8

9

10

11

12

Total Number of Combinations

Sum of the Dice Possible Combinations


2 (1, 1) 1

3 (1, 2) (____, ____) 2

4

5

6

7

8

9

10

11

12

Total Number of Combinations

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b) Create a bar graph showing the Sum of the Dice versus Number of Combinations.• Include a title.• Title the y-axis, Number of Combinations.• Title the x-axis, Sum of the Dice.• Choose an appropriate scale for the y-axis.

c) Which sum has the highest theoretical probability

of being rolled? ________

d) Does your answer to part c) match your experimental

results? YES ____ NO ____

e) Why do you think this is the case?

______________________________________________

______________________________________________

______________________________________________

4. When you roll 2 dice, list all of the combinations that make a sum of 7 or greater.

______________________________________________

______________________________________________

______________________________________________

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5. a) Complete the table.• Write the fractions in lowest terms.• Round each percent to the nearest whole number.

Sum of the Dice


Fraction of the Total


Percent of the Total


2 1 1 _ 36

2.777 = 3%

3 2

4

5

6

7

8

9

10

11

12

Total

b) List the pairs of sums that have the same theoretical

probability of occurring.

______________________________________________

c) The likelihood of rolling a total of 3 with 2 dice is the same as the total of the likelihood of rolling 2 other combinations. What are those 2 combinations?

____ and ____

d) As a percent, what is the chance of rolling 2 dice and

obtaining a total of 7 or greater? ____

Tech Tip:Suppose that you made 5 rolls. You rolled 2 twice.Use your calculator

to show 2 _

5 as a

percent. If your calculator has a

% key, enter

2 ÷ 5 % 2 is 40% of 5.

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6. a) Addalloftheclass’sresultsfrom#2a)andrecordthedataintheappropriaterowofthetallycolumn.Calculatethepercentofthetotalforeachsum.

Sum ofthe Dice Class Tally

Percent of Total

2

3

4

5

6

7

8

9

10

11

12

Total For Class Results

b)Graphtheresults.•Includeatitle.•Titlethey-axis,

PercentofTotal.•Titlethex-axis,

SumoftheDice.

✓ Check Your Understanding

1. Whichgraphiscloserinshapetothegraphin#3?

Thegraphin#2orthegraphin#6?______

2. Whydoyouthinkthisisso?

______________________________________________

______________________________________________

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1.4 Heads, Heads, Heads Focus: experimental probability, number sense

Warm Up

1. What is the theoretical probability of flipping a coin and getting tails?

2. If you flipped a coin 40 times, how many tails would you expect to get?

3. A weather forecast states that there is a 30% chance of rain. Is it likely or not likely to rain?

4. Write 3 _ 4 as a decimal and as a

percent.

Decimal: __________

Percent: __________

5. What is the theoretical probability of picking a heart from a standard deck of cards? Write your answer as a fraction and a percent.

Fraction: __________

Percent: __________

6. You flip a coin 25 times and get 8 heads. What is the experimental probability of getting heads? Write your answer as a fraction and a percent.

Fraction: __________

Percent: __________

Flipping Coins

• In this activity, you will flip 3 coins at the same time.• Getting 3 heads is called a “successful” result.• Any other result is called “unsuccessful.”• You will flip the set of 3 coins exactly 40 times.• The 40 flips are a sample. A sample is a small group of

results taken from a larger group. A sample is easy to analyse. You could flip the coins 8 million times. That would be a much larger sample.

1. a) You are going to flip 3 coins 40 times. How many

successful results do you expect? ______

b) Explain your answer to part a).

____________________________________________

____________________________________________

Go to pages 1–2 to write the definition for sample in your own words.

Go to pages 1–2 to write the definition for sample in your own words.

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2. a)Flipall3coinsexactly40times.Recordyourresultsinthetable.

Successful(Got 3 heads)

Unsuccessful(Did not get 3 heads)

Tally

Total

b)Howmanysuccessfulresultsdidyouget?______

Showthisasafractionofthetotalsample.______

c) Statethenumberofsuccessfulresults

asapercent.______

3. Inthechartbelow,listordrawallofthepossibleoutcomesforflipping3coinsatonce.

First Coin Second Coin Third Coin

4. a) Whatisthetheoreticalprobabilityofasuccessfulresult?Showyouranswerasafractionandapercent.

b)Whatisthetheoreticalprobabilityofanunsuccessfulresult?Showyouranswerasafractionandapercent.

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5. a) Record the individual results of the class from #2a) in the table. Add the class results for “Successful” and “Unsuccessful.”

b) How many flips are in this sample?

____ students × 40 flips each = ______ flips

c) Calculate the overall percent of successful results.

d) Create a circle graph showing the results from part a).• Estimate the size of each fraction of the circle.• Include a title.• Label each sector.

Successful Unsuccessful

Individual Results

Total

Successful Unsuccessful

Individual Results

Total

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1.

a) Thecartoonshowstheresultsoftheboy’sfirstflip.

Doyouagreewithhiscomment?YES____NO____

b) Explainyouranswertoparta).Usethetermsampleinyourexplanation.

______________________________________________

2. a) Whichclassmemberhadthegreatestnumber

ofsuccessfulresultsinthesamplein#2?__________

b) Whatwasthepercentofsuccessfulflips?_______

3. a) Whichclassmemberhadthelowestpercent

ofsuccessfulresultsin#2?___________

b) Whatwasthepercentofsuccessfulflips?_______

4. Howdoyouthinksamplesizerelatestotheoreticalprobability?

______________________________________________

______________________________________________

5. Ifyouflipped3coins8milliontimes,howmanysuccessfulresultswouldyouexpecttoget?

6. Explainyouranswerto#5.________________________

______________________________________________

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1.5 Free Coffee Focus: experimental probability, simulation

Warm Up

1. The theoretical probability of winning a prize in a lottery is 1 in 5. Write this as a fraction and a percent.

2. The weather report says there is a 70% chance of snow. Write the probability of it snowing as a decimal and a fraction.

3. You roll 2 dice. Circle the probability of rolling a sum of 7.

Impossible Not LikelyLikely

Very Likely Certain

4. Explain your answer to #3.

__________________________

__________________________

__________________________

__________________________

5. What is the theoretical probability of rolling a 5 with 2 dice? Write your answer as a fraction and a percent.

6. If you flip a coin 10 times, what is the theoretical probability of flipping heads? Write your answer as a fraction and a decimal.

7. Flip a coin 10 times. What is the experimental probability of flipping heads? Write your answer as a fraction and a decimal.

8. What is the difference between theoretical and experimental probability?

__________________________

__________________________

__________________________

__________________________

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It’s On the Cup

1. Acoffeeshoppromotionoffersprizesinspeciallymarkedcups.Thechanceofwinningis1in9.

a) Inyourownwords,explainthemeaningof“Thechanceofwinningis1in9.”

______________________________________________

______________________________________________

b) List2wordsthatmeanthesameas“chance.”

____________________________________________

c) Whatexperimentthatyoucompletedrecentlyhasthesametheoreticalprobabilityasgettingawinningcup?

______________________________________________

2. a) Howcanyousimulatethecoffeecuppromotionwithoutactuallyusingcoffeecups?Tosimulatemeanstomodelwithanexperiment.Describeordrawwhatyouwilldo.

______________________________________________

______________________________________________

______________________________________________

b) Ifyourunthissimulation100times,howmany

“winners”shouldyouget?_______

c) Explainhowyoudeterminedyouranswertopartb).

______________________________________________

______________________________________________

______________________________________________

Checkoutthe tableyoucompletedonpage23.

Checkoutthe tableyoucompletedonpage23.

Gotopages1–2towritethedefinitionforsimulate inyourownwords.

Gotopages1–2towritethedefinitionforsimulate inyourownwords.

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d) Test your hypothesis. Do the simulation exactly 100 times. Tally the results below.

Winner

Non-Winner

e) Write your winning results 3 ways.

As a percent of the total: ________

As a fraction of the total: _______

As a decimal: ________

f) Some people like to show data like this on a graph. Use a circle graph to display your results.

g) Did your experiment match the theoretical probability of the promotion?

YES ____ NO ____

h) If not, explain why.

______________________________________________

______________________________________________

______________________________________________

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•Anotherwaytorunthiskindofsimulationistouseadevicethatgeneratesrandomnumbers.

•Arandom number generatorisatoolthatpicksnumberssothateachnumberhasanequalprobabilityofcominguponeachtry.

•Agraphingcalculatorcanbesetuptoworkasarandomnumbergenerator.Itcanthenmodelthepreviousexperiment.

Gotopages1–2towritethedefinitionforrandom number generatorinyourownwords.

Gotopages1–2towritethedefinitionforrandom number generatorinyourownwords.

Tech Tip: Using the Random Number Generator in a TI-83/84 Graphing Calculator

1.PressMATH.ScrollrightsothatPRBishighlighted.

2.Press5toselect5:randInt(.ThecommandrandInt( tellsthecalculatortogeneraterandomintegers.

3.Type1,9).Makesuretherearenospacesbetweenthecharacters.Thistellsthecalculatortoselectnumbersbetween1and9.

4. PressENTER.Anintegerfrom1to9willbedisplayed.ContinuepressingENTERtogeneratemorerandomintegers.

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3. a) Select a target number from 1 to 9 for this

experiment. _____

Every time the random generator comes up with that number, you are a winner.

b) Use a random number generator to select exactly 100 numbers ranging from 1 to 9. Tally the results below.

Winner

Non-Winner

c) How many times did the number you selected in

part a) appear? ____

d) State your winning percent. ________

e) Explain your results in terms of simulating winning a prize from the coffee promotion.

______________________________________________

______________________________________________

4. a) Repeat the experiment another 100 times. Tally the results below.

Winner

Non-Winner

b) Add these results to you totals from #3b).

How many times did the number you selected in #3a)

appear? ________

c) State your winning percent. ________

d) Is your result closer to the theoretical probability you

calculated in #2b)? YES ____ NO ____

e) Explain your answer to part b). __________________

______________________________________________

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5. a) Collectthenumberofwinningsimulationsin#4b)fromeveryoneinyourclass.

Number of Winning Simulations forEach Member of the Class

Total Number of Winners in the Class = ________

b)Whatisthetotalnumberofrandomnumbers

generatedbytheclass?________

c) Calculatetheclass’swinningpercent.


1. Accordingtothetheoreticalprobabilityofthepromotion,howmanywinningresultsshouldyourclasshavehad?

2. Explainwhyyourindividualresultsandthewholeclass’sresultsmayhavediffered.

_______________________________________

_______________________________________

_______________________________________

3. Isthecoffeeshop’sadaccurate?Explain.

______________________________________________

______________________________________________

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1.6 What Are the Odds? Focus: probability, media, number sense

Warm Up

1. The probability of picking the 7 of clubs from a deck of cards

is 1 in ____.

2. The probability of picking any red card from a deck of cards

is 1 in ____.

3. What is the probability of flipping “tails, tails, tails” with 3 coins?

4. Reduce the following fractions to lowest terms.

a) 5 _ 10

b) 70 _ 100

What Are Odds? You flip a coin.

The probability of flipping heads is

# of chances of winning

__ # of possible flips

1 _ 2 .

Another way of showing this is 1:2. heads tails

The odds of flipping heads are # of chances of winning

__ # of chances of losing

1 _ 1 .

Another way of showing this is 1:1. heads tails

This can be confusing because the term odds is often used in the media as another word for probability or chance.

Go to pages 1–2 to write the definition for odds in your own words.

Go to pages 1–2 to write the definition for odds in your own words.

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•Anadsuchasthefollowingreallymeansthattheprobabilityofwinningis1in10(or10%).

•Theoddsofwinningwouldbe1:9. chanceofwinning chanceofnotwinning

1. a) Calculatetheoddsofdrawingaredcardfromadeckofcards.

Howmanyredcardsareinthedeck?____

____Howmanynotredcardsareinthedeck?____

=____

Oddsareshownasaratio.Theoddsare1:___.

b) Whataretheoddsofdrawingaspadefrom

adeckofcards?Theoddsare1:___.

c) Whataretheoddsofdrawinganacefromadeckofcards?

d) Whataretheoddsofdrawingajack,queen,orkingfromadeckofcards?

e) Whataretheoddsofrollinga3withonedie?

f) Whataretheoddsofflipping“heads,heads”with2coins?

g)Whataretheoddsofflipping“tails,tails,tails”with3coins?

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Populations

2. Collect the following data.

a) What is the student population of your school? ______

b) What is the grade 9 population? ______

c) What is the grade 10 population? ______

d) What is the grade 11 population? ______

e) What is the grade 12 population? ______

f) How many teachers are there? ______

g) How many teachers are male? ________

h) How many teachers are female? ________

i) How many other people work in the school? _______

j) Therefore, what is the total population of

the school? _______

3. What are the odds that the next teacher to walk past your classroom will be male?

4. Determine the following ratios. Whenever possible, write the ratios in simplest form.

a) The ratio of grade 9s to grade 10s: _____________

b) The ratio of grade 9s to grade 12s: _____________

c) The ratio of grade 11s to grade 12s: ____________

d) The ratio of students to teachers: ______________

e) The ratio of teachers to other people who work

in the school:______________

You have now worked with your school’s population. Go to pages 1–2 to write a definition for population in your own words.

You have now worked with your school’s population. Go to pages 1–2 to write a definition for population in your own words. Look at the glossary for help.Look at the glossary for help.

Simplify a ratio of 4 : 8 by dividing both numbers by 4. 4 : 8 = 1 : 2

Simplify a ratio of 4 : 8 by dividing both numbers by 4. 4 : 8 = 1 : 2

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Samples

Theschoolprincipalwantstodoasurveyaboutstartingandfinishingtheschoolday3hourslaterthanthecurrentstartandendtimes.

5. a) Thiswouldmakeyourschooldaystartat_____and

finishat_____.

b) Explainwhytheprincipalmightnotwishtosurveytheentirepopulationoftheschool.

______________________________________________

______________________________________________

•Theprincipaldecidestosurveyasampleoftheschoolpopulation.

•Asampleispartofapopulation.•Agoodsamplerepresentstheentirepopulation.

6. Theprincipalistryingtodecidewhichofthefollowingsampleswouldbestrepresenttheschool’spopulation.•Consideryourschool’spopulation.•Readthedescriptionofeachproposedsample.•Decidewhichonesarepotentiallygoodsamples.•Whichonesarepotentiallybadsamples?

Proposed Sample

Good Sample

Bad Sample

a) Surveyallofthegrade9s.

b) Surveyalloftheteachers.

c) Survey10studentsfromeachgradeandask10teachers.

d) Survey10%ofthepopulation.

e) Surveyonlythoseoldenoughtovote.

f) Survey10%ofthepopulationofeachgrade,theteachers,andtheotherstaff.

g) Surveythestudentsinthecafeteria.

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7. Choose 1 proposed sample you classified as a “Bad Sample.” Explain your thinking.

______________________________________________

______________________________________________

8. a) Describe a good sample of your school’s population.

______________________________________________

______________________________________________

b) Discuss your sample idea with several other students. Listen to their coaching to make sure that your sample plan represents the school’s population. Revise your sample if necessary.

______________________________________________

______________________________________________

c) Using the sample, conduct a small survey to determine whether the odds are likely or unlikely that your school’s population is in favour of starting and finishing the school day 3 hours later. Record your results.

In Favour

Not in Favour

d) What can you conclude from your survey?

______________________________________________

______________________________________________

Probability in the Media

Many people read long-term forecasts before making plans.

• Can we play volleyball outside on Monday?• Will it be warm enough to ride our bikes on Wednesday?• Should we plan a weekend beach party?

The long-term forecast on the next page shows the type of information the media provide.

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Long-Term Forecast

MondaySept.13

TuesdaySept.14

Wednesday Sept.15

Thursday Sept.16

FridaySept.17

SaturdaySept.18

P.O.P.

HighLow

Cloudy With Sunny

Breaks

Showers Isolated Showers

Mostly Sunny Sunny Sunny

40% 80% 60% 20% 20% 10%18°C 16°C 17°C 18°C 21°C 22°C11°C 13°C 9°C 14°C 16°C 18°C

24-Hr

Raincloseto1mm closeto10mm closeto5mm

9. a) WhatdoesP.O.P.standfor?

______________________________________________

b) Howcanithelpyouplanoutdoorjobsorevents?

______________________________________________

______________________________________________

c) Whichday,inyouropinion,wouldbebestforafamilybarbecue?Explainwhy.

______________________________________________

______________________________________________

d) Youworkforacompanythatpavesdriveways.Listthedaysyouthinkyouwillbeabletoworkthisweek.

______________________________________________


1. Jacksays,“Theoddsofa6-dayforecastbeingrightareslimtonone.”Whatmighthemeanbythis?

______________________________________________

______________________________________________

Hint:P.O.P.hastwoPs.Onestandsforthetopicofthischapter.Theotherisanotherwordforrain.

Hint:P.O.P.hastwoPs.Onestandsforthetopicofthischapter.Theotherisanotherwordforrain.

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Chapter 1 Review

1. Define theoretical probability.

______________________________________________

______________________________________________

2. What is the probability of each of the following?

a) picking the 9 of clubs from a deck of cards _________ (fraction)

b) flipping heads with a coin _________ (decimal)

c) picking a diamond from a deck of cards _________ (percent)

d) rolling a 3 with 1 die _________ (fraction)

e) rolling an even number with 1 die _________ (decimal)

f) flipping heads or tails with a coin _________ (percent)

3. a) How many combinations can be obtained by rolling 2 dice? ____

b) List all of the combinations for rolling a 7 with 2 dice.

______________________________________________

c) Write the probability of rolling a 7 as a fraction of the total.

4. Define experimental probability.

______________________________________________

______________________________________________

5. Pick 10 cards from a deck of 52.

a) How many spades did you pick? _________

b) Write the number of spades you got as a fraction, a decimal, and a percent.

__________ = __________ = __________fraction decimal percent

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6. Completethetable.


a) 1_2

b) 1_10

c) 0.3

d) 0.7

e) 90%

f) 95%

7. a) Createandlabelabargraphforthe“perfectworld”resultsforobtainingeachsuitwhenyoucutadeckofcards40times.

b) Thegraphinparta)shows__________________probability.

8. Adepartmentstoreoffers“scratchandwin”ticketstoitscustomers.Thestoreclaimsthat25%oftheticketsresultincustomerspayingnotaxesonpurchases.

a) Writetheprobabilityofgettingawinningticketasa

fraction.______

b) Ifthestoreprints10000tickets,howmanywinningticketsarethere?

c) Whataretheoddsofgettingawinningticket?

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Chapter 1 Practice Test

1. Explain the difference between theoretical probability and experimental probability.

_____________________________________________________

_____________________________________________________

_____________________________________________________

2. What is the theoretical probability of each of the following?

a) picking a club from a deck of cards _______ (fraction)

b) picking a spade or a heart from a deck of cards _______ (fraction)

c) flipping tails with a coin _______ (percent)

d) rolling a 7 with 1 die _______ (percent)

e) rolling an odd number with 1 die _______ (decimal)

3. a) How many combinations can you get by rolling 2 dice? _______

b) List all of the combinations for rolling 10, 11, or 12 with 2 dice.

_____________________________________________________

_____________________________________________________

c) Write the probability of rolling a 10 or greater as a fraction of the total.

d) Write the answer to part c) in lowest terms. _______

4. Roll a die 20 times.

a) How many 6s did you roll? _______

b) Write the number of 6s that you rolled as a fraction, a decimal, and a percent.

__________ = __________ = __________fraction decimal percent

c) This is an example of ___________________ probability.

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5. Completethetable.


a) 1_4

b) 1_5

c) 0.4

d) 0.65

e) 80%

6. Createandlabelabargraphforthe“perfectworld”resultsforrolling2diceexactly36times.Whattotalsdoyouget?

7. a) Youflip4coinsatthesametime.Whatdifferentwayscanthecoinsland?Listallcombinations.

b) Whatistheprobabilityofgettingallheadswith4coins?Explainhowyouknow.

_____________________________________________________

_____________________________________________________

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Task: Play Klass Kasino

The following activity is designed to simulate the way that many games of chance are set up. You don’t have to play.

The goal of any lottery, casino, or other gambling game is to have some winners and a lot of losers. While the games are designed to entertain, their main goal is to make money. Lots of it.

In this game, each student who wishes to participate has a calculator and enters the number 100. This represents the maximum number of points each student has to wager.

• You have 100 points to wager. Enter 100 in a calculator. • For each round, you choose how many points you wish to wager. • In this game, your teacher will cut a deck of cards to reveal 1 card.• You can play 1 of 4 games on each cut of the cards. The games are:

– Pick the Colour– Pick the Suit– Pick the Value– Pick the Card

• Each game has a different set of point values.– Pick the Colour: If you correctly pick the colour of the card showing,

you win 1 point for each point wagered. Add your winnings to the total on your calculator.

– Pick the Suit: If you correctly pick the suit of the card, you win 2 points for each point wagered. Add your winnings to the total on your calculator.

– Pick the Value: If you correctly pick the value of the card, you win 8 points for each point wagered. Add your winnings to the total on your calculator.

– Pick the Card: If you correctly pick the exact card showing, you win 20 points for each point wagered. Add your winnings to the total on your calculator.

• If you lose a game, deduct the number of points wagered from the total on your calculator.

Documents

Date 1 Probability - Algonquin Achievement Centrejoansavoie.weebly.com/.../chapter_1_-_probability.pdf · 2020-02-01 · Date 978-0-07-090894-9 Chapter 1 Probability • MHR Chapter