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978-0-07-090894-9 Chapter1Probability•MHR�
Chapter
1
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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?
_____________________________________________________
Date
� MHR • Chapter 1 Probability 978-0-07-09089�-9
Chapter
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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- .
Date
978-0-07-090894-9 SkillsPractice1:Fractions,Decimals,andPercents•MHR�
Chapter
1
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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
Date
� MHR • Chapter 1 Probability 978-0-07-090894-9
Chapter
1
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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 ______
Date
978-0-07-090894-9 What’stheChance?•MHR7
Chapter
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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).
______________________________________________
______________________________________________
______________________________________________
______________________________________________
Date
� MHR • Chapter 1 Probability 97�-0-07-090�94-9
Chapter
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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
.
Date
978-0-07-090894-9 What’stheChance?•MHR9
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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%
_____________________________________
_____________________________________
_____________________________________
_____________________________________
_____________________________________
Date
10 MHR • Chapter 1 Probability 978-0-07-090894-9
Chapter
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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%.
Date
978-0-07-090894-9 1.2InaPerfectWorld•MHR11
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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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12 MHR • Chapter 1 Probability 978-0-07-090894-9
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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 __________%
Date
978-0-07-090894-9 1.2InaPerfectWorld•MHR13
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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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14 MHR • Chapter 1 Probability 978-0-07-090894-9
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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.
Date
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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
Date
16 MHR • Chapter 1 Probability 978-0-07-090894-9
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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.
Date
978-0-07-090894-9 SkillsPractice2:EquivalentFractions•MHR17
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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_
Date
18 MHR • Chapter 1 Probability 978-0-07-090894-9
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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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20 MHR • Chapter 1 Probability 978-0-07-090894-9
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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
Number of 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.
______________________________________________
______________________________________________
______________________________________________
978-0-07-090894-9 1.3 Roll the Bones • MHR 21
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22 MHR • Chapter 1 Probability 978-0-07-090894-9
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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
Number of Combinations
Fraction of the Total
Number of Combinations
Percent of the Total
Number of Combinations
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.
Date
978-0-07-090894-9 1.3RolltheBones•MHR23
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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?
______________________________________________
______________________________________________
Date
24 MHR • Chapter 1 Probability 978-0-07-090894-9
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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.
Date
978-0-07-090894-9 1.4Heads,Heads,Heads•MHR25
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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.
Date
26 MHR • Chapter 1 Probability 978-0-07-090894-9
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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
Date
978-0-07-090894-9 1.4Heads,Heads,Heads•MHR27
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✓Check Your Understanding
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.________________________
______________________________________________
Date
28 MHR • Chapter 1 Probability 978-0-07-090894-9
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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?
__________________________
__________________________
__________________________
__________________________
Date
978-0-07-090894-9 1.5FreeCoffee•MHR29
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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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30 MHR • Chapter 1 Probability 978-0-07-090894-9
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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.
______________________________________________
______________________________________________
______________________________________________
Date
978-0-07-090894-9 1.5FreeCoffee•MHR31
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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.
Date
32 MHR • Chapter 1 Probability 978-0-07-090894-9
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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). __________________
______________________________________________
Date
978-0-07-090894-9 1.5FreeCoffee•MHR33
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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.
✓Check Your Understanding
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.
______________________________________________
✓Check Your Understanding
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.
Fraction Decimal Percent
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.
Fraction Decimal Percent
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.
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